Identifier
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-1
[]=>.
[1,0]=>[.,.]
[1,0,1,0]=>[[.,.],.]
[1,1,0,0]=>[.,[.,.]]
[1,0,1,0,1,0]=>[[[.,.],.],.]
[1,0,1,1,0,0]=>[[.,.],[.,.]]
[1,1,0,0,1,0]=>[[.,[.,.]],.]
[1,1,0,1,0,0]=>[.,[[.,.],.]]
[1,1,1,0,0,0]=>[.,[.,[.,.]]]
[1,0,1,0,1,0,1,0]=>[[[[.,.],.],.],.]
[1,0,1,0,1,1,0,0]=>[[[.,.],.],[.,.]]
[1,0,1,1,0,0,1,0]=>[[[.,.],[.,.]],.]
[1,0,1,1,0,1,0,0]=>[[.,.],[[.,.],.]]
[1,0,1,1,1,0,0,0]=>[[.,.],[.,[.,.]]]
[1,1,0,0,1,0,1,0]=>[[[.,[.,.]],.],.]
[1,1,0,0,1,1,0,0]=>[[.,[.,.]],[.,.]]
[1,1,0,1,0,0,1,0]=>[[.,[[.,.],.]],.]
[1,1,0,1,0,1,0,0]=>[.,[[[.,.],.],.]]
[1,1,0,1,1,0,0,0]=>[.,[[.,.],[.,.]]]
[1,1,1,0,0,0,1,0]=>[[.,[.,[.,.]]],.]
[1,1,1,0,0,1,0,0]=>[.,[[.,[.,.]],.]]
[1,1,1,0,1,0,0,0]=>[.,[.,[[.,.],.]]]
[1,1,1,1,0,0,0,0]=>[.,[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,0]=>[[[[[.,.],.],.],.],.]
[1,0,1,0,1,0,1,1,0,0]=>[[[[.,.],.],.],[.,.]]
[1,0,1,0,1,1,0,0,1,0]=>[[[[.,.],.],[.,.]],.]
[1,0,1,0,1,1,0,1,0,0]=>[[[.,.],.],[[.,.],.]]
[1,0,1,0,1,1,1,0,0,0]=>[[[.,.],.],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,0]=>[[[[.,.],[.,.]],.],.]
[1,0,1,1,0,0,1,1,0,0]=>[[[.,.],[.,.]],[.,.]]
[1,0,1,1,0,1,0,0,1,0]=>[[[.,.],[[.,.],.]],.]
[1,0,1,1,0,1,0,1,0,0]=>[[.,.],[[[.,.],.],.]]
[1,0,1,1,0,1,1,0,0,0]=>[[.,.],[[.,.],[.,.]]]
[1,0,1,1,1,0,0,0,1,0]=>[[[.,.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,0]=>[[.,.],[[.,[.,.]],.]]
[1,0,1,1,1,0,1,0,0,0]=>[[.,.],[.,[[.,.],.]]]
[1,0,1,1,1,1,0,0,0,0]=>[[.,.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,0]=>[[[[.,[.,.]],.],.],.]
[1,1,0,0,1,0,1,1,0,0]=>[[[.,[.,.]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,0]=>[[[.,[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,0]=>[[.,[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,0,1,0]=>[[[.,[[.,.],.]],.],.]
[1,1,0,1,0,0,1,1,0,0]=>[[.,[[.,.],.]],[.,.]]
[1,1,0,1,0,1,0,0,1,0]=>[[.,[[[.,.],.],.]],.]
[1,1,0,1,0,1,0,1,0,0]=>[.,[[[[.,.],.],.],.]]
[1,1,0,1,0,1,1,0,0,0]=>[.,[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,0,0,1,0]=>[[.,[[.,.],[.,.]]],.]
[1,1,0,1,1,0,0,1,0,0]=>[.,[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,1,0,0,0]=>[.,[[.,.],[[.,.],.]]]
[1,1,0,1,1,1,0,0,0,0]=>[.,[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,0]=>[[[.,[.,[.,.]]],.],.]
[1,1,1,0,0,0,1,1,0,0]=>[[.,[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,0,1,0]=>[[.,[[.,[.,.]],.]],.]
[1,1,1,0,0,1,0,1,0,0]=>[.,[[[.,[.,.]],.],.]]
[1,1,1,0,0,1,1,0,0,0]=>[.,[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,0,1,0]=>[[.,[.,[[.,.],.]]],.]
[1,1,1,0,1,0,0,1,0,0]=>[.,[[.,[[.,.],.]],.]]
[1,1,1,0,1,0,1,0,0,0]=>[.,[.,[[[.,.],.],.]]]
[1,1,1,0,1,1,0,0,0,0]=>[.,[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,0,1,0]=>[[.,[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,0,1,0,0]=>[.,[[.,[.,[.,.]]],.]]
[1,1,1,1,0,0,1,0,0,0]=>[.,[.,[[.,[.,.]],.]]]
[1,1,1,1,0,1,0,0,0,0]=>[.,[.,[.,[[.,.],.]]]]
[1,1,1,1,1,0,0,0,0,0]=>[.,[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],.],.],[.,.]],.]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[.,.],.],.],[[.,.],.]]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[.,.],.],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[.,.],.],[.,.]],[.,.]]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[.,.],.],[[.,.],.]],.]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,.],.],[[[.,.],.],.]]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,.],.],[.,[.,.]]],.]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,.],.],[[.,[.,.]],.]]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,.],.],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[.,.],[.,.]],.],.],.]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[[[[.,.],[.,.]],.],[.,.]]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,.],[.,.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[[[[.,.],[[.,.],.]],.],.]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,.],.]],[.,.]]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[.,.],.],.]],.]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[.,.],.],.],.]]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,.],[.,.]]],.]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,.],[.,.]],.]]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[[.,.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,.]]],.],.]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,.]],.]],.]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[[.,.],[[[.,[.,.]],.],.]]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,.],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[.,.],.],.]]]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[[.,.],[.,[[.,[.,.]],.]]]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,.]],.],.],.],.]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[.,.]],.],.],[.,.]]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,.]],.],[.,.]],.]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[[[.,[.,.]],.],[[.,.],.]]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,.]],.],.]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,.],.]],.]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,.],.],.]]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,.]]],.]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[.,.],.]],.],.],.]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[.,.],.]],.],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],.]],[.,.]],.]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,.],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[[.,.],.]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[.,.],.],.]],.],.]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],.],.]],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[.,.],.],.],.]],.]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[.,.],.],.],[.,.]]]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[.,.],.],[.,.]]],.]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[.,.],.],[.,.]],.]]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,.],.],[[.,.],.]]]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[.,.],[.,.]]],.],.]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[.,.],[.,.]],.]],.]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[.,.],[.,.]],.],.]]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,.],[[.,.],.]]],.]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[.,.],.],.]]]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,.]]],.],.],.]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[.,.]]],.],[.,.]]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,.]]],[.,.]],.]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,[.,.]]],[[.,.],.]]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[.,.]],.]],.],.]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,.]],.]],[.,.]]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[.,.]],.],.]],.]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[.,.]],.],.],.]]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[.,.]]],.]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[.,.]],.]]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[.,.],.]]],.],.]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,.],.]]],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,.],.]],.]],.]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],.]],.],.]]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[.,.],.],.]]],.]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[.,.],.],.]],.]]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[.,.],.],.],.]]]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[.,.],[.,.]]]],.]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[.,.],[.,.]]],.]]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[.,[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,.]]]],.],.]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,.]]],.]],.]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[.,.]]],.],.]]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[.,.]]],[.,.]]]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,.]],.]]],.]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[.,.]],.]],.]]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,.]],.],.]]]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[.,.],.]]]],.]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[.,.],.]]],.]]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[.,.],.]],.]]]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,.]]],.]]]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[.,.]],.]]]]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[.,.],.],.],.],[.,.]],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[.,.],.],.],.],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[.,.],.],.],[.,.]],.],.]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[.,.],.],.],[[.,.],.]],.]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[.,.],.],.],[[[.,.],.],.]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[[[.,.],.],.],[[.,[.,.]],.]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[.,.],.],[.,.]],.],.],.]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[[[[.,.],.],[[.,.],.]],.],.]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[[[.,.],.],[[[.,.],.],.]],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[[[.,.],.],.],.]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[[.,.],.],[[[.,.],[.,.]],.]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[[[.,.],.],[[.,[.,.]],.]],.]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[[.,.],.],[[[.,[.,.]],.],.]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[[[.,.],.],[.,[[.,.],.]]],.]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,.],.],[[.,[[.,.],.]],.]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[[.,.],.],[[.,[.,[.,.]]],.]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[[.,.],.],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[.,.]],.],.],.],.]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[[[[.,.],[[.,.],.]],.],.],.]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[[[.,.],[[.,.],.]],.],[.,.]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[[[.,.],[[.,.],.]],[.,.]],.]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[[[.,.],[[[.,.],.],.]],.],.]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[.,.],.],.],.]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[.,.],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],[[[.,.],.],[.,.]]],.]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[.,.],[[[[.,.],.],[.,.]],.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[[[.,.],[[.,.],[.,.]]],.],.]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[[.,.],[.,.]],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[.,.],[[[[.,.],[.,.]],.],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,.],.]]],.]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,.],.]],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[[.,.],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],[.,[.,.]]],.],.],.]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[[[.,.],[[.,[.,.]],.]],.],.]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,[.,.]],.]],[.,.]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[[.,[.,.]],.],.]],.]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[.,.],[[[[.,[.,.]],.],.],.]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,[.,.]],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,[.,.]],[.,.]],.]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,[[.,.],.]]],.],.]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,.],.]],.]],.]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[.,.],[[[.,[[.,.],.]],.],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[[.,.],.]],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[.,.],.],.]]],.]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[.,.],[[.,[[[.,.],.],.]],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[[.,.],.],.],.]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[.,.]]],.]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,[.,.]]]],.],.]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,[.,.]]],.]],.]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[.,.],[[[.,[.,[.,.]]],.],.]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[[.,.],[.,[[.,[.,.]],.]]],.]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[.,.]],.]],.]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[.,.],[.,[[[.,[.,.]],.],.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[[.,.],[.,[.,[[.,.],.]]]],.]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[.,[[.,.],.]]],.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[.,.],[.,[[.,[[.,.],.]],.]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,.]],.],.],.],.],.]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[.,[.,.]],.],.],[.,.]],.]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[.,[.,.]],.],[.,.]],.],.]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[[.,.],.]],.]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,[.,.]],.],[.,[.,.]]],.]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[.,[.,.]],[.,.]],.],.],.]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[[.,[.,.]],[[.,.],.]],.],.]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[.,.],.],.]],.]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,.],[.,.]]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[.,.]]],.],.]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,[.,.]],.]],.]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],.],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[[.,.],.]]],.]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[[.,.],.]],.],.],.],.]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[[.,.],.]],.],.],[.,.]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[[.,.],.]],.],[.,.]],.]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,[[.,.],.]],.],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[.,.],.]],[.,.]],.],.]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[.,.]],[.,.]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[.,.],.]],.]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,[[.,.],.]],[.,[.,.]]],.]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[[.,.],.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[[.,.],.],.]],.],.],.]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[[.,.],.],.]],.],[.,.]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[[.,.],.],.]],[.,.]],.]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[[[.,.],.],.]],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[[[.,.],.],.]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[[.,.],.],.],.]],.],.]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[[.,.],.],.],.]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[.,.],.],.],.],.]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[[.,.],.],.],[.,.]]],.]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[.,.],.],.],[.,.]],.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[[.,.],.],[.,.]]],.],.]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[.,.],.],[.,.]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[[.,.],.],[.,.]],.]],.]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[[.,.],.],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[.,.],.],[.,.]],[.,.]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[[[.,.],.],[[.,.],.]]],.]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[[[.,.],.],[[.,.],.]],.]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[[[.,.],.],[.,[.,.]]]],.]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[[[.,.],.],[.,[.,.]]],.]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,.],.],[[.,[.,.]],.]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[[.,.],[.,.]]],.],.],.]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,[[.,.],[.,.]]],.],[.,.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],[.,.]]],[.,.]],.]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[[.,.],[.,.]],.]],.],.]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],[.,.]],.]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[[.,.],[.,.]],.],.]],.]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[[.,.],[.,.]],.],.],.]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[[[.,.],[.,.]],.],[.,.]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[[.,.],[.,.]],[.,.]]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,.],[.,.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,[[.,.],[[.,.],.]]],.],.]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[[[.,.],[[.,.],.]],.]],.]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[[[.,.],[[.,.],.]],.],.]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,.],.]],[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,.],[[[.,.],.],.]]],.]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[.,[[[.,.],[[[.,.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,.],[.,[.,.]]]],.],.]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],[.,[.,.]]],.]],.]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[.,[[[[.,.],[.,[.,.]]],.],.]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[[.,.],[[.,[.,.]],.]]],.]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[.,.]],.]],.]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[.,[[.,.],[[[.,[.,.]],.],.]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[.,[[.,.],[.,[[.,.],.]]]],.]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,.],[.,[[.,.],.]]],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,.],.]],.]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[.,[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,.]]],.],.],.],.]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[.,[.,.]]],.],.],[.,.]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,[.,.]]],.],[.,.]],.]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[.,[.,.]]],.],[[.,.],.]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[.,[.,.]]],[.,.]],.],.]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,[.,[.,.]]],[[.,.],.]],.]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[[.,.],.],.]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[.,[.,.]],.]],.],.],.]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],.],[.,.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,[.,.]],.]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,.],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[.,[.,.]],.],.]],.],.]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],.],.]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[.,[.,.]],.],.],.]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[.,.]],.],.],.],.]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[.,[.,.]],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[.,[.,.]],.],[.,.]]],.]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],.],[.,.]],.]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,[.,.]],.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[.,[.,.]],[.,.]]],.],.]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[.,[.,.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[.,[.,.]],[.,.]],.],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,.],.]]],.]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,.],.]],.]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[[.,.],.],.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[[.,.],.]]],.],.],.]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[[.,.],.]]],.],[.,.]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[[.,.],.]]],[.,.]],.]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,[[.,.],.]]],[[.,.],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[[.,.],.]],.]],.],.]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[[.,.],.]],.],.]],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[[.,.],.]],.],.],.]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[.,.],.]],.],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[[.,.],.]],[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[.,.]],.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,.],.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[[.,.],.],.]]],.],.]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[[.,.],.],.]]],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,.],.],.]],.]],.]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[[.,.],.],.]],.],.]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[[.,.],.],.]],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[[.,.],.],.],.]]],.]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,.],.],.],.]],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[.,.],.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[[.,.],.],.],[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[[.,.],.],[.,.]]]],.]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[[.,.],.],[.,.]]],.]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[[.,.],.],[.,.]],.]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[[.,.],[.,.]]]],.],.]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,.],[.,.]]],.]],.]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],.]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[[.,.],[.,.]],.]]],.]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,.],[.,.]],.]],.]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[[.,.],[.,.]],.],.]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[.,[[.,.],[[.,.],.]]]],.]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,.],.]]],.]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[.,[.,[[[.,.],[[.,.],.]],.]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[.,[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,[.,.]]]],.],.],.]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[.,[.,.]]],.]],.],.]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[.,[.,.]]],.],.]],.]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[.,[.,.]]],.],.],.]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[.,[.,.]],.]]],.],.]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[.,.]],.]],.]],.]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[.,.]],.]],.],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[.,[.,.]],.],.]]],.]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],.],.]],.]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[.,[.,.]],.],.],.]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[[.,.],.]]]],.],.]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[[.,.],.]]],.]],.]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[[.,.],.]]],.],.]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[[.,.],.]],.]]],.]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,.],.]],.]],.]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[[.,.],.]],.],.]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[[.,.],.],.]]]],.]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[[.,.],.],.]]],.]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[[.,.],.],.]],.]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[.,.],.],.],.]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[.,[.,.]]]],.],.]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[.,[.,.]]],.]],.]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[.,[.,.]],.]]],.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[.,[.,.]],.]],.]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[[[[.,.],.],.],[[.,[.,.]],.]],.]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[[[.,.],.],.],[[[.,[.,.]],.],.]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[[[.,.],.],.],[[.,[.,[.,.]]],.]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[[[[[.,.],.],[[.,.],.]],.],.],.]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[[[.,.],.],[[[.,.],.],[.,.]]],.]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[[[[.,.],.],[[.,.],[.,.]]],.],.]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[[[.,.],.],[[[.,.],[.,.]],.]],.]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[[.,.],.],[[[[.,.],[.,.]],.],.]]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[[.,.],.],[[.,.],[[.,[.,.]],.]]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[[[[.,.],.],[[.,[.,.]],.]],.],.]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[[.,.],.],[[[.,[.,.]],.],.]],.]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[[[.,[.,.]],.],.],.]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,.],.],[[[.,[.,.]],[.,.]],.]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[[[[.,.],.],[.,[[.,.],.]]],.],.]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[[[.,.],.],[[.,[[.,.],.]],.]],.]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[[.,.],.],[[[.,[[.,.],.]],.],.]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[[[.,.],.],[.,[[[.,.],.],.]]],.]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[[.,.],.],[[.,[[[.,.],.],.]],.]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[[[.,.],.],[.,[[.,.],[.,.]]]],.]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[[[.,.],.],[[.,[.,[.,.]]],.]],.]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[[.,.],.],[[[.,[.,[.,.]]],.],.]]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[[[.,.],.],[.,[[.,[.,.]],.]]],.]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,.],.],[[.,[[.,[.,.]],.]],.]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[[.,.],.],[.,[[[.,[.,.]],.],.]]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[[[.,.],.],[.,[.,[[.,.],.]]]],.]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[[.,.],.],[[.,[.,[[.,.],.]]],.]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[[.,.],.],[.,[[.,[[.,.],.]],.]]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[[.,.],[.,.]],.],[[.,[.,.]],.]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[[[.,.],[.,.]],[[.,.],.]],.],.]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],.]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],.]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],[[.,.],.]],.],[.,.]],.]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[[.,.],[[.,.],.]],[.,.]],.],.]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[[[.,.],[[[.,.],.],.]],.],.],.]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[[.,.],[[[.,.],.],.]],.],[.,.]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[[.,.],[[[.,.],.],.]],[.,.]],.]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[[.,.],[[[[.,.],.],.],.]],.],.]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],[[[[.,.],.],.],[.,.]]],.]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[.,.],[[[[[.,.],.],.],[.,.]],.]]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[[.,.],[[[.,.],.],[.,.]]],.],.]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[[[.,.],.],[.,.]],.]],.]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[[.,.],[[[.,.],.],[[.,.],.]]],.]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[[.,.],[[[.,.],.],[.,[.,.]]]],.]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],[[.,.],[.,.]]],.],.],.]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[[.,.],[.,.]]],.],[.,.]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[[.,.],[[[.,.],[.,.]],.]],.],.]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[[.,.],[.,.]],.]],[.,.]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[.,.],[.,.]],.],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[.,.],[.,.]],.],.],.]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[[.,.],[[.,.],.]],.]],.]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],.]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[.,.],[[[[.,.],[.,[.,.]]],.],.]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,[.,.]],.]]],.]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[[.,.],[[.,.],[.,[[.,.],.]]]],.]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[[.,.],[.,[[.,.],.]]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[[[.,.],[[.,[.,.]],.]],.],.],.]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[[.,.],[[.,[.,.]],.]],.],[.,.]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[[.,.],[[[.,[.,.]],.],.]],.],.]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[[[.,[.,.]],.],.]],[.,.]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[.,[.,.]],.],.],.]],.]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[.,[.,.]],.],.],.],.]]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],[[[.,[.,.]],.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[.,.],[[[[.,[.,.]],.],[.,.]],.]]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[[.,.],[[.,[.,.]],[.,.]]],.],.]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],.]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,[.,.]],[[.,.],.]]],.]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],[.,[[.,.],.]]],.],.],.]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[.,[[.,.],.]]],.],[.,.]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,[[.,.],.]]],[.,.]],.]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[[.,.],[[.,[[.,.],.]],.]],.],.]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[[.,[[.,.],.]],.],.]],.]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[.,.],[[[[.,[[.,.],.]],.],.],.]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,[[.,.],.]],.],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,[[.,.],.]],[.,.]]],.]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,[[.,.],.]],[.,.]],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,[[[.,.],.],.]]],.],.]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[[[.,.],.],.]]],[.,.]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[[.,.],.],.]],.]],.]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[.,.],[[[.,[[[.,.],.],.]],.],.]]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[[[.,.],.],.]],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[[.,.],.],.],.]]],.]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[.,.],[[.,[[[[.,.],.],.],.]],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[[.,.],[.,[[[.,.],.],[.,.]]]],.]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[[[.,.],.],[.,.]]],.]]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[.,.],[.,[[[[.,.],.],[.,.]],.]]]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[[.,.],[.,.]]]],.],.]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,.],[.,.]]],.]],.]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[.,.],[[[.,[[.,.],[.,.]]],.],.]]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[.,.],[.,.]],.]]],.]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[[.,.],[.,.]],.]],.]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[.,.],[.,[[[[.,.],[.,.]],.],.]]]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[[.,.],[.,[[.,.],[[.,.],.]]]],.]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,.],.]]],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[[.,.],[[.,[.,[.,.]]],.]],.],.]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[[.,[.,[.,.]]],.],.]],.]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,[[.,[.,.]],.]]],.],.]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,[.,.]],.]],.]],.]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[.,.],[[[.,[[.,[.,.]],.]],.],.]]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[.,[.,.]],.],.]]],.]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[.,.],[[.,[[[.,[.,.]],.],.]],.]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[[.,[.,.]],.],.],.]]]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,[[.,.],.]]]],.],.]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,[[.,.],.]]],.]],.]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[.,.],[[[.,[.,[[.,.],.]]],.],.]]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[[.,.],[.,[[.,[[.,.],.]],.]]],.]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],.]],.]]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[.,.],[.,[[[.,[[.,.],.]],.],.]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[[.,.],[.,[.,[[[.,.],.],.]]]],.]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[.,[[[.,.],.],.]]],.]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[.,.],[.,[[.,[[[.,.],.],.]],.]]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[.,.],[.,[[.,[.,[.,.]]],.]]],.]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[.,[.,.]],.],.],[[.,.],.]],.]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[[[.,[.,.]],.],.],[[.,[.,.]],.]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[.,[.,.]],.],[.,.]],.],.],.]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[[[[.,[.,.]],.],[[.,.],.]],.],.]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[[[.,.],.],.]],.]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[[[.,[.,.]],.],[[.,.],[.,.]]],.]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[[[[.,[.,.]],.],[.,[.,.]]],.],.]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[[.,[.,.]],.]],.]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[[[.,[.,.]],.],[.,[[.,.],.]]],.]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],.]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[[[[.,[.,.]],[[.,.],.]],.],.],.]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[[[.,[.,.]],[[.,.],.]],.],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],[[.,.],.]],[.,.]],.]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[[[.,[.,.]],[[[.,.],.],.]],.],.]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[[.,.],.],.],.]],.]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[[[.,.],.],[.,.]]],.]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[[.,.],.],[.,.]],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[[.,.],[.,.]]],.],.]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[[.,.],[.,.]],.]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],.],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,[[.,.],.]],.]],.]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,[[.,.],.]],.],.]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[[[.,.],.],.]]],.]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[.,[[.,.],.]],.],.],[.,.]],.]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,[[.,.],.]],.],.],[.,[.,.]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[.,[[.,.],.]],.],[.,.]],.],.]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[[.,[[.,.],.]],.],[.,.]],[.,.]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[[.,[[.,.],.]],.],[[.,.],.]],.]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,[[.,.],.]],.],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,[[.,.],.]],.],[.,[.,.]]],.]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,[[.,.],.]],.],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,[[.,.],.]],.],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[.,[[.,.],.]],[.,.]],.],.],.]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[[.,[[.,.],.]],[.,.]],.],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],.]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[[.,[[.,.],.]],[[.,.],.]],.],.]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[[.,.],.],.]],.]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,[[.,.],.]],[[.,.],[.,.]]],.]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[.,[[.,.],.]],[.,[.,.]]],.],.]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],.]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[.,[[.,.],.]],[[[.,[.,.]],.],.]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],.]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[[[.,.],.],.]],.],[.,.]],.]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[.,[[[.,.],.],.]],.],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[[.,.],.],.]],[.,.]],.],.]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[[.,.],.],.]],[[.,.],.]],.]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,[[[.,.],.],.]],[.,[.,.]]],.]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[[.,.],.],.]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[[[.,.],.],.],.]],.],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[[[.,.],.],.],.]],[.,.]],.]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[[[[.,.],.],.],.]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[[[.,.],.],.],.],.]],.],.]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[[[.,.],.],.],.],.]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[[.,.],.],.],.],.],.]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[[[.,.],.],.],.],[.,.]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[[.,.],.],.],.],[.,.]],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[[[.,.],.],.],[.,.]]],.],.]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[[.,.],.],.],[.,.]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[[[.,.],.],.],[.,.]],.]],.]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[[[.,.],.],.],[.,.]],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[[.,.],.],.],[.,.]],[.,.]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[[[[.,.],.],.],[[.,.],.]]],.]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[[[[.,.],.],.],[[.,.],.]],.]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[[.,.],.],.],[[.,[.,.]],.]]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[[[.,.],.],.],[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[[[.,.],.],[.,.]]],.],.],.]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,[[[.,.],.],[.,.]]],.],[.,.]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,[[[.,.],.],[.,.]]],[.,.]],.]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[[[.,.],.],[.,.]],.]],.],.]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[[.,.],.],[.,.]],.]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[[[.,.],.],[.,.]],.],.]],.]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],.],[.,.]],.],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[[[[.,.],.],[.,.]],.],[.,.]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[[[.,.],.],[.,.]],[.,.]]],.]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[[.,.],.],[.,.]],[.,.]],.]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[[[.,.],.],[.,.]],[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,[[[.,.],.],[[.,.],.]]],.],.]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[[[.,.],.],[[.,.],.]]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[[[[.,.],.],[[.,.],.]],.]],.]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[[[[.,.],.],[[.,.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[.,[[[[.,.],.],[[.,.],.]],[.,.]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[.,[[[[.,.],.],[[[.,.],.],.]],.]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[[[.,.],.],[[.,.],[.,.]]],.]]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[[.,.],.],[[[.,.],[.,.]],.]]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[.,[[[.,.],.],[.,[.,.]]]],.],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[.,[[[[.,.],.],[.,[.,.]]],.]],.]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[.,[[[[[.,.],.],[.,[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[[[.,.],.],[[.,[.,.]],.]]],.]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,.],.],[[.,[.,.]],.]],.]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[.,[[[.,.],.],[[[.,[.,.]],.],.]]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[.,[[[.,.],.],[.,[[.,.],.]]]],.]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[[[.,.],.],[.,[[.,.],.]]],.]]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[[.,.],.],[[.,[[.,.],.]],.]]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[[.,.],[.,.]]],.],.],.],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[[.,.],[.,.]]],.],.],[.,.]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[[.,.],[.,.]]],.],[.,.]],.]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[[.,.],[.,.]]],.],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[.,.],[.,.]]],[.,.]],.],.]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[.,.],[.,.]]],[[.,.],.]],.]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[[.,.],[.,.]],.]],.],.],.]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[[.,.],[.,.]],.]],.],[.,.]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[[.,.],[.,.]],.]],[.,.]],.]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[[.,.],[.,.]],.]],[[.,.],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[[.,.],[.,.]],.],.]],.],.]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[[.,.],[.,.]],.],.]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[.,.],[.,.]],.],.],.]],.]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],[.,.]],.],.],.],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[.,.],[.,.]],.],.],[.,.]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[[.,.],[.,.]],.],[.,.]]],.]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[.,.],[.,.]],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[.,.],[.,.]],.],[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[[.,.],[.,.]],[.,.]]],.],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[[.,.],[.,.]],[.,.]],.]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[[.,.],[.,.]],[.,.]],.],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[[.,.],[.,.]],[[.,.],.]]],.]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[[.,.],[.,.]],[[.,.],.]],.]]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[[.,.],[[.,.],.]]],.],.],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[.,[[.,.],[[.,.],.]]],.],[.,.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],[[.,.],.]]],[.,.]],.]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[[.,.],[[.,.],.]],.]],.],.]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[[.,.],[[.,.],.]],.],.]],.]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[[.,.],[[.,.],.]],.],.],.]]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[[.,.],[[.,.],.]],.],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,.],[[.,.],.]],[.,.]],.]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[[.,.],[[.,.],.]],[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[[.,.],[[[.,.],.],.]]],.],.]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[[[.,.],.],.]]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[[.,.],[[[.,.],.],.]],.]],.]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[.,[[[[.,.],[[[.,.],.],.]],.],.]]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[[[.,.],.],.]],[.,.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,.],[[[[.,.],.],.],.]]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[[.,.],[[[[.,.],.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[[.,.],.],.],.],.]]]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[[[.,.],.],.],[.,.]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[.,[[.,.],[[[.,.],.],[.,.]]]],.]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[.,[[[.,.],[[[.,.],.],[.,.]]],.]]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,.],[[[[.,.],.],[.,.]],.]]]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,.],[[.,.],[.,.]]]],.],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],[[.,.],[.,.]]],.]],.]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[.,[[[[.,.],[[.,.],[.,.]]],.],.]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[[.,.],[[[.,.],[.,.]],.]]],.]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[[.,.],[.,.]],.]],.]]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[.,.],[.,.]],.],.]]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[[.,.],.]]],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[[.,.],[[.,.],.]],.]]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[[.,.],[.,[.,.]]]],.],.],.]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[[.,.],[.,[.,.]]],.]],.],.]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[.,[[[[.,.],[.,[.,.]]],.],.]],.]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[[.,.],[.,[.,.]]],.],.],.]]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[.,[[.,.],[[.,[.,.]],.]]],.],.]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],.]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[.,[[[[.,.],[[.,[.,.]],.]],.],.]]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[.,[[.,.],[[[.,[.,.]],.],.]]],.]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[.,[[[.,.],[[[.,[.,.]],.],.]],.]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[.,[.,.]],.],.],.]]]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,.],[.,[[.,.],.]]]],.],.]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],[.,[[.,.],.]]],.]],.]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[[.,.],[.,[[.,.],.]]],.],.]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[[.,.],.]],.]],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[.,[[.,.],[[[.,[[.,.],.]],.],.]]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[[.,.],[.,[[[.,.],.],.]]]],.]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[.,[[[.,.],[.,[[[.,.],.],.]]],.]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[[.,.],.],.]],.]]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[.,[[.,.],[.,[.,[.,.]]]]],.],.]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[.,[[.,.],[.,[[.,[.,.]],.]]]],.]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[.,[.,[.,.]]],.],.],[.,.]],.]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],.]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[[.,[.,[.,.]]],.],[[.,.],.]],.]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],.]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[[.,[.,[.,.]]],[[.,.],.]],.],.]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,[.,[.,.]]],[[[.,.],.],.]],.]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[[.,[.,.]],.]],.],.],[.,.]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[[.,[.,.]],.]],.],[.,.]],.]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[.,[[.,[.,.]],.]],.],[[.,.],.]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[.,[.,.]],.]],[.,.]],.],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[.,[.,.]],.]],[[.,.],.]],.]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[[.,[.,.]],.],.]],.],[.,.]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[[.,[.,.]],.],.]],[.,.]],.]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[[[.,[.,.]],.],.]],[[.,.],.]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[[.,[.,.]],.],.],.]],.],.]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[[.,[.,.]],.],.],.]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[.,[.,.]],.],.],.],.]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,[.,.]],.],.],.],.],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[.,[.,.]],.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[[.,[.,.]],.],.],[.,.]]],.]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[.,[.,.]],.],.],[.,.]],.]]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[[.,[.,.]],.],[.,.]]],.],.]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[[.,[.,.]],.],[.,.]],.]],.]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[[.,[.,.]],.],[.,.]],.],.]]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[[[.,[.,.]],.],[[.,.],.]]],.]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],.],[[.,.],.]],.]]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[[.,[.,.]],.],[[[.,.],.],.]]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[[.,[.,.]],[.,.]]],.],.],.]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],.],.]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[[.,[.,.]],[.,.]],.],.]],.]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[.,.]],[.,.]],.],.],.]]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,[[.,[.,.]],[[.,.],.]]],.],.]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[[[.,[.,.]],[[.,.],.]],.]],.]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[[[.,[.,.]],[[.,.],.]],.],.]]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[[[.,.],.],.]]],.]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[[.,.],.],.]],.]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[[[.,.],.],.],.]]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[[.,.],.]]],.],.],.],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[.,[[.,.],.]]],.],.],[.,.]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,[[.,.],.]]],.],[.,.]],.]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[.,[[.,.],.]]],.],[[.,.],.]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[.,[[.,.],.]]],[.,.]],.],.]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,[.,[[.,.],.]]],[[.,.],.]],.]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[.,[[.,.],.]],.]],.],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],.]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[.,[[.,.],.]],.],.]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[.,[[.,.],.]],.],.],.]],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[[.,.],.]],.],.],.],.]]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[.,[[.,.],.]],.],.],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[.,[[.,.],.]],.],[.,.]]],.]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[.,[[.,.],.]],.],[.,.]],.]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,[[.,.],.]],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[.,[[.,.],.]],[.,.]]],.],.]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[.,[[.,.],.]],[.,.]],.]],.]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[.,[[.,.],.]],[.,.]],.],.]]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],.]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[[.,.],.]],.]]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[.,[[.,[[.,.],.]],[[[.,.],.],.]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[[[.,.],.],.]]],.],.],.]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[[[.,.],.],.]]],.],[.,.]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[[[.,.],.],.]]],[.,.]],.]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[[[.,.],.],.]],.]],.],.]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[[.,.],.],.]],.]],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[[[.,.],.],.]],.],.]],.]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[[[.,.],.],.]],.],.],.]]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[[.,.],.],.]],.],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[[[.,.],.],.]],[.,.]]],.]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[[.,.],.],.]],[.,.]],.]]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[[.,.],.],.]],[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[.,[[.,[[[.,.],.],.]],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[[[.,.],.],.],.]]],.],.]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[[[.,.],.],.],.]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[[.,.],.],.],.]],.]],.]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[[[.,.],.],.],.]],.],.]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[[[.,.],.],.],.]],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[[[.,.],.],.],.],.]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[[[.,.],.],.],.],.]],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[[.,.],.],.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[[[.,.],.],.],.],[.,.]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[[[.,.],.],.],[.,.]]]],.]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[[[.,.],.],.],[.,.]]],.]]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[[[.,.],.],.],[.,.]],.]]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[[.,.],.],.],[[.,.],.]]]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[[[.,.],.],[.,.]]]],.],.]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,.],.],[.,.]]],.]],.]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[[.,.],.],[.,.]]],.],.]]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[[[.,.],.],[.,.]],.]]],.]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,.],.],[.,.]],.]],.]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[[[.,.],.],[.,.]],.],.]]]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[[.,.],.],[.,.]],[.,.]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[.,[[[.,.],.],[[.,.],.]]]],.]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[.,[[[.,.],.],[[.,.],.]]],.]]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[.,[.,[[[[.,.],.],[[.,.],.]],.]]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[[.,.],[.,.]]]],.],.],.]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[[.,.],[.,.]]],.]],.],.]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[[.,.],[.,.]]],.],.]],.]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[[.,.],[.,.]]],.],.],.]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[[.,.],[.,.]],.]]],.],.]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,.],[.,.]],.]],.]],.]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[[.,.],[.,.]],.]],.],.]]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[[.,.],[.,.]],.],.]]],.]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,.],[.,.]],.],.]],.]]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[.,.],[.,.]],.],.],.]]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[[.,.],[[.,.],.]]]],.],.]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],.]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],[[.,.],.]]],.],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[[.,.],[[.,.],.]],.]]],.]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,.],[[.,.],.]],.]],.]]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[[.,.],[[.,.],.]],.],.]]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[.,[[.,.],[[[.,.],.],.]]]],.]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[[.,.],.],.]]],.]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[.,[.,[[[.,.],[[[.,.],.],.]],.]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[.,[[.,.],.]]]],.]]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[.,[.,[.,.]]],.]],.],[.,.]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[.,[.,[.,.]]],.],.],.]],.]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[.,[.,.]]],.],.],.],.]]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[[.,[.,.]],.]]],.],.],.]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[[.,[.,.]],.]],.],.]],.]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[[.,[.,.]],.]],.],.],.]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[.,[.,.]],.]],.],[.,.]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[[.,[.,.]],.],.]]],.],.]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,[.,.]],.],.]],.]],.]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[[.,[.,.]],.],.]],.],.]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[[.,[.,.]],.],.],.]]],.]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,[.,.]],.],.],.]],.]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[.,[.,.]],.],.],.],.]]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[.,[.,[[[.,[.,.]],[[.,.],.]],.]]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,[[.,.],.]]]],.],.],.]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[.,[[.,.],.]]],.]],.],.]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[.,[[.,.],.]]],.],.]],.]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[.,[[.,.],.]]],.],.],.]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[.,[[.,.],.]]],[.,.]],.]]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[.,[[.,.],.]],.]]],.],.]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[[.,.],.]],.]],.],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[.,[[.,.],.]],.],.]]],.]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[[.,.],.]],.],.]],.]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[.,[[.,.],.]],.],.],.]]]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[[[.,.],.],.]]]],.],.]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[[[.,.],.],.]]],.]],.]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[[[.,.],.],.]]],.],.]]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[[[.,.],.],.]],.]]],.]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[[.,.],.],.]],.]],.]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[[[.,.],.],.]],.],.]]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],.]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[[[.,.],.],.],.]]],.]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[[[.,.],.],.],.]],.]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[[.,.],.],.],.],.]]]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[[.,.],[.,.]]]]],.],.]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[[.,.],[.,.]]]],.]],.]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[[.,.],[.,.]]]],.],.]]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[[.,.],[[.,.],.]]]],.]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[[.,[.,.]],.]],.],.]]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[.,[[.,.],.]]]],.],.]]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]],.]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]],.]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]],.]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]],.]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]],.]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]],.]
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[[.,.],[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,[[.,.],.]],.]]]]]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]],.]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]],.]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]],.]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]],.]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]],.]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]],.]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[[.,.],[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[[.,.],[.,[.,[[.,[.,[[.,.],.]]],.]]]]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[[.,[.,.]],.],.]]]]]
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]],.]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]],.]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[[[.,.],.],.],.]]]]],.]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]],.]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[[.,.],[.,[.,[[.,[[.,[.,.]],.]],.]]]]
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[[.,[.,[.,.]]],[.,.]]]]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[[[.,.],.],.],.]]]]]
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[[.,.],[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]],.]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[[[.,.],.],.]],.]]]],.]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]],.]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]],.]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]],.]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[[.,.],[[[.,.],.],.]]]]],.]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[[.,.],[[.,[.,[.,[.,[[.,.],.]]]]],.]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[.,.],[.,[[.,[.,[[.,[.,.]],.]]],.]]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[.,[.,[.,.]]],.],.]]]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[[.,.],[.,[.,[[.,[[[.,.],.],.]],.]]]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[[.,[[.,.],.]],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[[.,.],[[[.,.],.],.]]]]]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[.,.],[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]],.]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,[[[.,.],.],.]]],.]]],.]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[[.,[.,[[.,.],[.,[[[.,.],.],.]]]]],.]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]],.]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]],.]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],[.,.]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],[.,.]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[[.,.],[.,[[.,[.,[[[.,.],.],.]]],.]]]
[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[[.,.],[.,[[.,.],[.,[[[.,.],.],.]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[.,.],[[.,.],[.,[.,[[.,[.,.]],.]]]]]
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.],.]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.],.]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,[[[.,.],.],.]]]],.]],.]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]],.]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]],.]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[[[.,[.,.]],.],.],.]]]],.]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0]=>[[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]],.]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[[[[.,.],.],.],[.,.]]]]],.]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]],.]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]],.]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],[.,.]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],[.,.]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[[.,.],[.,[[[.,[.,[.,[.,.]]]],.],.]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[[.,.],[.,[[.,[[.,.],[[.,.],.]]],.]]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[[.,.],[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[[.,[.,.]],.],.],.]]]]
[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[[.,.],[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[[[[.,.],.],.],[.,.]]]]]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[[[.,.],.],.]]]]]
[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[.,.],[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[[[.,.],.],.],.],.],[.,.]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[[[[.,.],.],.],.],[.,.]],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[[[.,.],.],.],.],[.,.]],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[[[[[.,.],.],.],.],[[.,.],.]],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[[[[.,.],.],.],.],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[[[.,.],.],.],.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[[[[[.,.],.],.],.],[.,[.,.]]],.]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[[[.,.],.],.],.],[[.,[.,.]],.]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[[[[.,.],.],.],.],[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[[[[.,.],.],.],.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[[[[.,.],.],.],[.,.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[[[[[.,.],.],.],[.,.]],.],[.,.]]]
[1,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[[[[.,.],.],.],[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[[[[[.,.],.],.],[[.,.],.]],.],.]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[[[.,.],.],.],[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[.,[[[[.,.],.],.],[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[.,[[[[.,.],.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[.,[[[[[[.,.],.],.],[.,[.,.]]],.],.]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[.,[[[[.,.],.],.],[[[.,[.,.]],.],.]]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[[[[.,.],.],.],[.,[[.,.],.]]],.]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[[[.,.],.],.],[[.,[[.,.],.]],.]]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[.,[[[[.,.],.],.],[.,[[[.,.],.],.]]]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[.,[[[[[.,.],.],.],[.,[.,[.,.]]]],.]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[.,[[[[.,.],.],.],[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[.,[[[[.,.],.],.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[.,.],.],[.,.]],.],.],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[[.,.],.],[.,.]],.],.],[.,.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[[.,.],.],[.,.]],.],[.,.]],.]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[[.,.],.],[.,.]],.],[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[[[.,.],.],[.,.]],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[[[.,.],.],[.,.]],[[.,.],.]],.]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[.,[[[[.,.],.],[.,.]],[[[.,.],.],.]]]
[1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],.],[[.,.],.]],.],.],.]]
[1,1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[.,[[[[.,.],.],[[.,.],.]],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[.,[[[[[.,.],.],[[[.,.],.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[[.,.],.],[[[[[.,.],.],.],.],.]]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[[[.,.],.],[[[[.,.],.],.],[.,.]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[.,[[[[[.,.],.],[[.,.],[.,.]]],.],.]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[.,[[[.,.],.],[[.,.],[[[.,.],.],.]]]]
[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[.,[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],.],[.,[.,.]]],.],.],.]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[.,[[[[[.,.],.],[[.,[.,.]],.]],.],.]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[.,[[[.,.],.],[[[[.,[.,.]],.],.],.]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[[[.,.],.],[.,[[.,.],.]]],.],.]]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[.,[[[.,.],.],[[[.,[[.,.],.]],.],.]]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[.,[[[.,.],.],[[.,[[[.,.],.],.]],.]]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[.,[[[.,.],.],[.,[[[[.,.],.],.],.]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[.,[[[.,.],.],[[[.,[.,[.,.]]],.],.]]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[.,[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[.,[[[.,.],.],[.,[[[.,[.,.]],.],.]]]]
[1,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[.,[[[.,.],.],[.,[.,[[[.,.],.],.]]]]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[.,[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]]
[1,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[.,[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]]
[1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[.,[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[[.,.],[.,.]],.],.],.],[.,.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[[.,.],[.,.]],.],.],[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[[[.,.],[.,.]],.],[.,.]],.],.]]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[[[[.,.],[.,.]],.],[[.,.],.]],.]]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[[[.,.],[.,.]],.],[[[.,.],.],.]]]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[[[[.,.],[.,.]],.],[.,[.,.]]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],[.,.]],[.,.]],.],.],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[[[[.,.],[.,.]],[.,.]],.],[.,.]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[[[.,.],[.,.]],[.,.]],[[.,.],.]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[[.,.],[.,.]],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,.],[.,.]],[[.,[.,.]],.]],.]]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[[.,.],[.,.]],[[.,[[.,.],.]],.]]]
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],[[.,.],.]],.],.],.],.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[.,.],[[.,.],.]],.],.],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[.,.],[[.,.],.]],.],[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[[.,.],[[.,.],.]],[.,.]],.],.]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[[.,.],[[.,.],.]],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[[.,.],[[[.,.],.],.]],.],.],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[[.,.],[[[[[.,.],.],.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[[[[.,.],.],.],.],[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[.,[[.,.],[[[[.,.],.],.],[[.,.],.]]]]
[1,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[.,[[.,.],[[[[.,.],.],.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[[.,.],[[[.,.],.],[.,[.,.]]]],.]]
[1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[[[.,.],[.,.]],.],[.,.]]]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[.,[[.,.],[[.,.],[[[[.,.],.],.],.]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[.,[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[[.,.],[[.,[.,.]],.]],.]]]
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],[.,[.,.]]],.],.],.],.]]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[.,.],[.,[.,.]]],.],[[.,.],.]]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[.,[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[[.,.],[[.,[.,.]],.]],[[.,.],.]]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[[.,[.,.]],.],.],.],.]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[[.,.],[.,[[.,.],.]]],.],.],.]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[.,[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[.,[[[.,.],[[[.,[[.,.],.]],.],.]],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[.,[[.,.],.]],.],.],.]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[[.,.],[.,[[[.,.],.],.]]],.],.]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[.,[[.,.],[[[.,[[[.,.],.],.]],.],.]]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[.,[[[.,.],[.,[[[[.,.],.],.],.]]],.]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[[[.,.],.],.],.]],.]]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[[.,.],[.,[[[[[.,.],.],.],.],.]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[[.,.],[.,[.,[.,.]]]],.],.],.]]
[1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[.,[.,[.,.]]],.],.],.]]]
[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[.,[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[[.,[.,.]],.]],.]],.]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[.,[[.,.],[[[.,[[.,[.,.]],.]],.],.]]]
[1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[.,[[.,.],[.,[[[[.,[.,.]],.],.],.]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[.,[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[.,[[.,.],[.,[[[.,[[.,.],.]],.],.]]]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[.,[[[.,.],.],.]]],.]]]
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[[.,.],[.,[.,[[[[.,.],.],.],.]]]]]
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[.,[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[.,[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]]
[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[.,[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]]
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[.,[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]]
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[.,[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[.,[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]]
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[.,[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]]
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[.,[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[[.,[.,.]],.],.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[[.,[.,.]],.],.],.],[.,.]],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[[.,[.,.]],.],.],.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[[.,[.,.]],.],.],.],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[[[.,[.,.]],.],.],[.,.]],.],.]]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[[[.,[.,.]],.],.],[[[.,.],.],.]]]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[[.,[.,.]],.],[[[[.,.],.],.],.]]]
[1,1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[.,[[[.,[.,.]],.],[.,[[[.,.],.],.]]]]
[1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[.,[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[.,[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,[.,.]],[.,.]],.],.],.],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[[.,[.,.]],[.,.]],[.,.]],.],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[.,.]],[[.,.],.]],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[.,.]],[[.,.],.]],.],.],.]]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[[.,[.,.]],[[.,.],.]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[[[[.,.],.],.],.],.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[[.,[.,.]],[[[[.,.],.],.],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[.,[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[.,[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[.,.]],[.,[.,.]]],.],.],.]]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[[[.,[.,.]],.],.],.]]]
[1,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[.,[[.,[.,.]],[.,[[[[.,.],.],.],.]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[.,[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]]
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[.,[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]]
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[.,[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[.,[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[.,[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[.,[[.,.],.]],.],.],.],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[.,[[.,.],.]],.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[[.,[[.,.],.]],.],[[[.,.],.],.]]]
[1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[[.,.],.]],[.,.]],.],.],.]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[[.,[.,.]],.]],.]]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[.,[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[[[.,.],.],.]],.],.],.],.]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[.,[[[.,.],.],.]],.],.],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,[[[.,.],.],.]],.],[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[.,[[[.,[[[.,.],.],.]],.],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[.,[[.,[[[.,.],.],.]],[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[[[[.,.],.],.],.]],.],.],.]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[[[.,.],.],.],.]],.],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[.,[[.,[[[[.,.],.],.],.]],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[[[[.,.],.],.],.],.]],.],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[[[[.,.],.],.],.],.]],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[[[[.,.],.],.],.],[.,.]]],.]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[[[[.,.],.],.],.],[.,.]],.]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[[[.,.],.],.],.],[[.,.],.]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[[[[.,.],.],.],.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[[[.,.],.],.],[.,.]]],.],.]]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[[[[.,.],.],.],[.,.]],.],.]]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[.,[[[[.,.],.],.],[[.,.],.]]],.]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[.,[.,[[[[.,.],.],.],[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[[[[.,.],.],.],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[[[.,.],.],.],[.,[.,.]]]],.]]
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[.,[.,[[[[.,.],.],.],[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[[[.,.],.],[.,.]]],.],.],.]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[[.,.],.],[.,.]],.],.],.]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[[.,.],.],[[.,.],.]]],.],.]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[.,[.,[[[[.,.],.],[[[.,.],.],.]],.]]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[[[.,.],.],[[[[.,.],.],.],.]]]]
[1,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[[[.,.],.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[[[.,.],.],[.,[.,.]]]],.],.]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[[[.,.],.],[.,[.,.]]],.],.]]]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[.,[.,[[[[.,.],.],[.,[[.,.],.]]],.]]]
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[[[.,.],.],[.,[[[.,.],.],.]]]]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[.,[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]]
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[[.,.],[.,.]]],.],.],.],.]]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[[.,.],[.,.]],.],.],.],.]]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,.],[.,.]],[.,.]],.]],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[[.,.],[[.,.],.]]],.],.],.]]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[.,.],[[.,.],.]],.],.],.]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],[[[.,.],.],.]]],.],.]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[[.,.],[[[.,.],.],.]],.],.]]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[.,.],[[[.,.],.],.]],[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[[[.,.],.],.],.]]],.]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[.,[.,[[[.,.],[[[[.,.],.],.],.]],.]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]]
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[[.,.],[[[[.,.],.],.],[.,.]]]]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[[.,.],[.,.]],.]]],.]]
[1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[[.,.],[[.,.],[[[.,.],.],.]]]]]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]]
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[[.,.],[.,[.,.]]]],.],.],.]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]]
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[.,[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[[.,.],[.,[[.,.],.]]],.],.]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[.,[.,[[[.,.],[[.,[[.,.],.]],.]],.]]]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[.,[.,[[[.,.],[.,[[[.,.],.],.]]],.]]]
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[.,[.,[[.,.],[[.,[[[.,.],.],.]],.]]]]
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[[.,.],[.,[[[[.,.],.],.],.]]]]]
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[.,[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]]
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[.,[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]]
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[.,[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]]
[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[.,[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[.,[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]]
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]]
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[.,[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[.,[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]]
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]]
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[.,[.,[.,.]]],.],.],.],[.,.]]]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[.,[.,[.,.]]],.],.],[[.,.],.]]]
[1,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[[.,[.,[.,.]]],.],[[[.,.],.],.]]]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]]
[1,1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[.,[.,.]]],[.,.]],.],.],.]]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]]
[1,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[.,[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[.,[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]]
[1,1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[.,[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]]
[1,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[.,[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[.,[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]]
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[.,[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[[.,[.,.]],.]],.],.],.],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]]
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[[[.,[.,.]],.],.]],.],.],.]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[[[.,[.,.]],.],.],.]],.],.]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[[[.,[.,.]],.],.],.]],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[[[.,[.,.]],.],.],.],.]],.]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[[[.,[.,.]],.],.],.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[[.,[.,.]],.],.],[[.,.],.]]]]
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[.,[.,[[[[.,[.,.]],.],[[.,.],.]],.]]]
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[.,[.,.]],[.,.]],.],.],.]]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[[.,[.,.]],[[[[.,.],.],.],.]]]]
[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[.,[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]]
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[.,[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]]
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[.,[[.,.],.]]],.],.],.],.]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[.,[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,[[.,.],.]],.],.],.]],.]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[.,[[.,.],.]],.],.],.],.]]]
[1,1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[.,[[.,.],.]],.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[.,[[[.,.],.],.]]],.],.],.]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,[[[.,.],.],.]]],.],[.,.]]]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[.,[[[.,.],.],.]]],[[.,.],.]]]
[1,1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[.,[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[[[.,.],.],.]],.]],.],.]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,[[[.,.],.],.]],.]],[.,.]]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[[[.,.],.],.]],.],.]],.]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[.,[[[.,.],.],.]],.],.],.]]]
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[.,[.,[[.,[[[.,.],.],.]],[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[[[[.,.],.],.],.]]],.],.]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[[[[.,.],.],.],.]]],[.,.]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[[[[.,.],.],.],.]],.],.]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[[[[.,.],.],.],.]],[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[[[[.,.],.],.],.],.]]],.]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[[[[.,.],.],.],.],.]],.]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[[[.,.],.],.],.],[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[[[[.,.],.],.],[.,.]]]],.]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[[[[.,.],.],.],[.,.]],.]]]]
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[[[.,.],.],.],[[.,.],.]]]]]
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[[[.,.],.],[.,.]]]],.],.]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[[.,.],.],[.,.]],.],.]]]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[[[.,.],.],[[.,.],.]]]],.]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[[[.,.],.],[[.,.],.]],.]]]]
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[[.,.],.],[[[.,.],.],.]]]]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]]
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]]
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[.,[[.,.],[.,.]]]],.],.],.]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[.,.],[[.,.],.]],.],.]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[[.,.],[[[.,.],.],.]]],.]]]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]]
[1,1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]]
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]]
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]]
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]]
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]]
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]
[1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]]
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[.,[.,[.,.]]]],.],.],.],.]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0]=>[.,[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,0]=>[.,[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[[.,[.,[.,.]]],.]],.],.],.]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[[.,[.,[.,.]]],.],.]],.],.]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,[.,[.,.]]],.],.],.]],.]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[.,[.,[.,.]]],.],.],.],.]]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]]
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]]
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0]=>[.,[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[.,[[.,[.,.]],.]]],.],.],.]]
[1,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,0]=>[.,[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[[.,[.,.]],.]],.]],.],.]]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[.,[[.,[.,.]],.]],.],.],.]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[[[.,[.,.]],.],.],.]],.]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]]
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]]
[1,1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[.,[.,[[.,.],.]]]],.],.],.]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]]
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0]=>[.,[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[.,[.,[[.,.],.]]],.],.],.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[.,[[.,.],.]],.],.],.]]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]]
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[[[.,.],.],.]]],.],.]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[.,[[[.,.],.],.]],.],.]]]]
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[[[[.,.],.],.],.]]],.]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[[[[.,.],.],.],.]],.]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]]
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]]
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]]
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[.,[[.,.],[.,.]]]]],.],.]]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[[.,.],[.,.]]]],.],.]]]
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]]
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]]
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]]
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0]=>[.,[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]]
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]]
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]]
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[.,[[.,[.,.]],.]],.],.]]]]
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,[[.,.],.]]]],.],.]]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]]
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]]
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]]
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]]
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[[[[.,.],.],.],.],[[[.,[.,.]],.],.]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[[[.,.],.],.],[[[[.,[.,.]],.],.],.]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[[[[.,[.,.]],.],.],.],.]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[[[[.,.],.],.],.],.],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[[[[.,.],.],.],.],[[.,[[.,.],.]],.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[[[.,.],.],.],[[[.,[[.,.],.]],.],.]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[[[[.,.],.],.],.],[[.,[.,[.,.]]],.]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[[[.,[[.,.],.]],.],.],.]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[[[.,.],.],.],[[[.,[.,[.,.]]],.],.]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[.,[[.,.],.]],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[[[[.,.],.],.],.],[.,[[[.,.],.],.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[[[.,.],.],.],[[.,[[[.,.],.],.]],.]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[[[[.,.],.],.],.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[[.,.],.],[[[.,[[[.,.],.],.]],.],.]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[[.,.],[[[[.,[[[.,.],.],.]],.],.],.]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[[.,.],.],[[[.,[[.,.],[.,.]]],.],.]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[[[.,.],.],.],[[.,[.,[[.,.],.]]],.]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[.,.],.],[[[.,[.,[[.,.],.]]],.],.]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[[.,.],[[[[.,[.,[[.,.],.]]],.],.],.]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[[[.,.],.],.],[.,[[[[.,.],.],.],.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[[[.,.],.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[[[.,.],.],.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[[.,.],[[[.,[[[.,.],.],[.,.]]],.],.]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[[.,.],.],[[[.,[.,[.,[.,.]]]],.],.]]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,.],.],[[.,[[.,.],[[.,.],.]]],.]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[[.,.],.],[[.,[.,[[[.,.],.],.]]],.]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[.,.],.],[.,[[[[[.,.],.],.],.],.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[.,.],[[.,[[[[[.,.],.],.],.],.]],.]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[.,.],.],[.,[[[[.,.],.],.],[.,.]]]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[[.,.],[[[.,[[.,.],[.,[.,.]]]],.],.]]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[[[.,.],.],[[.,.],.]]],.]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[.,.],.],[[.,[.,[[.,[.,.]],.]]],.]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[.,[[[[.,.],.],.],.]]],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[[[[.,.],.],.],.],.],.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[[[[.,.],.],.],.],[.,.]]]]
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[[.,.],.],[[.,[.,[.,[[.,.],.]]]],.]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,[.,.]],.]]],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[[.,.],[[[.,[.,[.,[.,[.,.]]]]],.],.]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[[.,.],[.,[[.,.],[[[[.,.],.],.],.]]]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[[[.,.],.],.],.],.]]]]
[1,0,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[[.,.],.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[[.,.],.],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[[[[[[.,.],.],.],.],[.,.]],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[[[.,.],.],.],.],[.,.]],[.,.]],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[[[[[[.,.],.],.],.],[.,[.,.]]],.],.]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[[[[[.,.],.],.],.],[.,[.,.]]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[[[.,.],.],.],.],[.,[.,[.,.]]]],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[[[[[[.,.],.],.],[.,.]],.],[.,.]],.]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[[[[[[.,.],.],.],[.,.]],[.,.]],.],.]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[[.,.],.],.],[.,.]],[.,.]],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[[[.,.],.],.],[.,[.,.]]],.],.],.]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[[[[[.,.],.],.],[.,[.,.]]],[.,.]],.]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[[[.,.],.],.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[.,.],.],[.,.]],.],.],.],[.,.]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[.,.],.],[.,.]],.],.],[.,.]],.]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[[.,.],.],[.,.]],.],.],[.,[.,.]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[[.,.],.],[.,.]],.],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[[.,.],.],[.,.]],[.,.]],.],.],.]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[[.,.],.],[.,.]],[.,.]],[.,.]],.]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[[[.,.],.],[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],.],[.,[.,.]]],.],.],.],.]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],[.,.]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[[[.,.],.],[.,[.,[.,.]]]],.],.],.]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[[[.,.],.],[.,[.,[.,[.,.]]]]],.],.]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[.,.],[.,.]],.],.],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[[.,.],[.,.]],.],.],.],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[[.,.],[.,.]],.],[.,.]],.],.],.]
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[[.,.],[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[[[[[.,.],[.,.]],[.,.]],.],.],[.,.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[[[[[.,.],[.,.]],[.,.]],[.,.]],.],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[[[[.,.],[.,.]],[.,.]],[.,[.,.]]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[[.,.],[.,.]],[.,[.,.]]],.],.],.]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,.],[.,[.,.]]],[.,.]],[.,.]],.]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[[.,.],[.,[.,.]]],[.,[.,.]]],.],.]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],[.,.]]
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[.,[.,[.,.]]]],.],.],.],.]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[[[[[.,.],[.,[.,[.,.]]]],[.,.]],.],.]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[[.,[.,.]],.],.],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[[.,[.,.]],.],.],.],[.,.]],.],.]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[[.,[.,.]],.],.],.],[.,.]],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[[.,[.,.]],.],.],.],[.,[.,.]]],.]
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[[.,[.,.]],.],.],.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[[.,[.,.]],.],.],[.,.]],.],.],.]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[[[.,[.,.]],.],.],[.,.]],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[[.,[.,.]],.],.],[.,[.,[.,.]]]],.]
[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[[.,[.,.]],.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[.,.]],.],[.,.]],.],.],.],.]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[.,[.,.]],[.,.]],.],.],.],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[[.,[.,.]],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[.,[.,.]],[.,.]],[.,.]],.],.],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[[.,[.,.]],[.,.]],[.,[.,.]]],.],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,.]],[.,[.,.]]],.],.],.],.]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[[.,[.,.]],[.,[.,[.,.]]]],.],.],.]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.],.]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[.,[.,[.,.]]],.],.],.],.],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[.,[.,[.,.]]],.],.],.],[.,.]],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[.,[.,[.,.]]],.],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],[.,.]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,[.,[.,.]]],.],[.,.]],[.,.]],.]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,[.,[.,.]]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,.]]],[.,[.,.]]],.],.],.]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],[.,.]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]],.]
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,[.,.]]]],[.,.]],.],.],.]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]],.]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.],.]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[[[.,.],.],.]],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[[[[.,.],.],.],.],.]],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[[[.,.],.],[.,.]]],.],.],.],.]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[[[[.,.],.],.],[.,.]]],.],.],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[[[[.,.],.],.],.],[.,.]]],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[.,[[.,.],.]],.],.],.],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[[.,.],[.,.]],.],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[[[[.,.],.],.],.],.],.]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[[[[.,.],.],.],.],.]]],.],.]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[[[[.,.],.],.],.]]],.],.],.]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[[[.,.],.],.]]],.],.],.],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[.,[.,[.,[.,.]]]],.]],.],.],.]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[[.,[.,[.,.]]],.]],.],.],.],.]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[[.,[.,.]],.]],.],.],.],.],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[[[[.,.],.],.],.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[[[.,.],.],.],.],.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,.],[[[[[.,.],.],.],.],.]]],.]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[[[.,.],.],.]],.],.],.],.]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],.],[[.,.],.]],.],.],.],.]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[[[[.,.],.],.],.]],.],.],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,.]],[[.,.],.]],.],.],.],.]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[[[.,[.,.]],.],.],.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[[[[[.,.],.],.],.],.]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[[[[.,.],.],.],.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[.,[[[.,.],.],.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[.,[[.,.],.]],[.,[.,[[[.,.],.],.]]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[.,[.,.]],[.,[.,[[[[.,.],.],.],.]]]]
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[.,[.,[.,.]]],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[[.,[.,[.,[.,.]]]],[.,[.,[[.,.],.]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[.,[.,[.,.]]],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[[[.,.],.],[.,.]],.],[[[.,.],.],.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],[.,.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0]=>[[.,[.,[[.,[.,[.,.]]],.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[.,[.,[.,.]]],[.,[.,[[.,[.,.]],.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[[[[[.,.],.],.],.],[[[.,.],.],.]],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[[[[[[.,.],.],.],.],[[.,.],.]],.],.]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[[.,[.,.]],.],.],[[[[.,.],.],.],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[[[[[.,.],.],.],.],[[.,.],.]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[[[[.,.],.],.],.],.]],[.,.]],.]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[[[.,.],.],.],.]],[.,.]],.],.]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[.,[[[.,.],.],.]],[.,.]],.],.],.]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[[.,.],.]],[.,.]],.],.],.],.]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,[[[.,.],[.,.]],[.,.]]],[.,.]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[[.,.],[.,.]],[.,.]],.]],[.,.]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[[.,.],[.,.]],.]],[.,.]],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],[[.,[.,.]],.]]],[.,.]],.]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[[[.,.],[.,.]],[[.,[.,.]],.]]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[[[.,.],[.,.]],[.,.]],.]],.],.]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[[.,.],[.,.]],.]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],[.,.]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],[.,.]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,[[[.,.],.],.]],.],[[[.,.],.],.]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[[[[.,.],.],.],.],.]]]],.]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[[[[.,.],.],.],.],[.,.]]]],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[.,[[.,.],.]],.],.],.],[.,.]],.]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[[.,.],.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[[[.,.],.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[[[[.,.],.],.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[[[[.,.],.],.],.],.],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[[[[.,.],.],.],.],.]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,.]]]],[[[[.,.],.],.],.]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,[.,[[.,.],.]]]],[[[.,.],.],.]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,[.,[[[.,.],.],.]]]],[[.,.],.]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[[[.,.],.],[[[.,.],.],.]]],.],.]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[.,[[[.,.],.],.]],.],[.,.]],.],.]
[1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[.,[.,[.,.]]],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[.,[.,[.,.]]],[.,[[.,[[.,.],.]],.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],[[[.,.],.],.]],.]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[[[.,.],.],.],.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,[.,[.,[[.,.],.]]]]],[[.,.],.]]
[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,[.,[[.,.],.]]],.],.],.],[.,.]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[.,[.,[[.,.],.]]]],.],.],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[.,[.,[[.,.],.]]]]],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[[[[[.,.],.],.],.],[.,[[.,.],.]]],.]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[.,.],[[[[[[.,.],.],.],[.,.]],.],.]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[[[.,.],.],[.,[[[.,.],.],.]]],.],.]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[[[[.,.],[.,.]],.],.],.]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[[.,.],.]],[[[[[.,.],.],.],.],.]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[[[.,[.,.]],.],.],[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[[.,.],.],[.,[[[.,[.,.]],.],[.,.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[[[.,.],.],.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],[.,[[[.,.],.],.]]],.],.],.]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[[[[.,.],.],[.,[[.,.],.]]],.],.],.]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,[[[.,.],.],.]]],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[[[.,.],.],.],.],.],[[.,.],.]],.]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[[[.,.],.],.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[[[[.,.],.],.],.],.]],.],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[[[[[.,.],.],.],.],.]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[.,.],.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[[.,[[.,.],.]],.]],.],.],.],.]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[[.,.],.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]],.]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.],.]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[.,[.,.]],[[.,.],[.,.]]],.],.],.]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],.]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,[[.,.],[.,.]]]],[.,.]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[.,[[.,.],.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]],.]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[[[.,[.,.]],.],.],[.,.]]]],.]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[.,[[.,.],.]],[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[[[.,.],.],[[.,.],.]],[[[.,.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[[.,.],[[[[.,.],.],.],.]],[[.,.],.]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[[.,[.,[[[[.,.],.],.],.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[[[.,.],.],.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[[[.,.],.],.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[[.,.],.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[[[.,.],.],[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[[[[.,.],.],.],.],[.,.]],.]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[[[[[.,.],.],.],.],[[.,.],.]]],.]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[[[.,.],.],.],.]],[[.,.],.]],.]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[[[[[.,.],.],.],.],[.,[.,.]]]],.]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[[.,[[[.,.],.],.]],.],.]],.]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[[[.,.],[.,[.,[[[[.,.],.],.],.]]]],.]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[[[[.,.],.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[[.,[.,.]],.],.],.],[[.,.],.]],.]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[.,[[.,.],.]],.],.],[[.,.],.]],.]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[[.,.],[.,.]],.],.],[[.,.],.]],.]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[[[.,.],.],.],.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[[[.,.],.],.],[[.,.],[[[.,.],.],.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[[.,.],.],[[.,.],[[[[.,.],.],.],.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[[[.,.],.],.],.],.]]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,[.,[[.,.],.]]],.],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[[[[[.,.],.],.],.],.]],[[.,.],.]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[.,[[.,.],[.,.]]]]],.],[.,.]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[.,[.,[.,[.,.]]]],.],.],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[.,[.,[[.,.],.]]]],.]],.],.]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[.,[[.,.],[.,.]]]],.]],.],.]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[.,[.,[.,[.,.]]]],.],.]],.],.]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[[[[.,.],.],.],.]]]],.],.]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[.,[[[.,.],.],.]]],.]],.],.]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[.,[.,[[.,.],.]]],.]],.],.],.]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[[.,[[.,.],[[.,[[.,.],[.,.]]],.]]],.]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[[.,[.,.]],.]],.],.],.],.]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[.,[[[.,.],.],.]],.],.],[.,.]],.]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[[[.,.],.],[[[.,[.,.]],.],.]],.],.]
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[[[.,.],[.,.]],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[[[.,.],[.,.]],.],.],[.,[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],.]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[[[.,[.,.]],[.,.]],[[.,.],.]],.],.]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,[[.,.],.]]],[.,.]],[.,.]],.]
[1,1,1,0,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[.,[.,[.,.]]],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[[[[.,.],.],.],.],[[[.,.],[.,.]],.]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[[[.,.],.],.],[[.,.],[[.,[.,.]],.]]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[[.,.],.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[[[[.,.],.],.],.]],.]]],.]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[.,[[.,.],[[[[.,.],.],.],.]]]],.]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.],.]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[[[[[.,.],.],.],.],[[.,.],[.,.]]],.]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[[.,[.,.]],.],.],.],[[[.,.],.],.]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[[.,.],[.,.]]],.],.],.],.]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[[.,.],.],[[.,.],[.,.]]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[[[[[.,.],.],.],[[.,.],[.,.]]],.],.]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[[.,[.,.]],.]]]],[.,[.,.]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[.,[[.,.],.]],.],[.,.]],.],.],.]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[[[.,[.,.]],.],.],.]],.],.],.]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[[[.,.],.],[.,.]],.],.]],.],.]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[[.,[.,.]],.],[[.,[.,[[.,.],.]]],.]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,[.,[.,.]]],.],[[.,[[.,.],.]],.]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,[.,[.,[.,.]]]],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[[[.,.],.],.]],[[[[.,.],.],.],.]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[[[[.,.],.],.],.],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[[.,.],.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[[[.,.],.],.],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[[.,[.,.]],[.,.]]]],.],.],.]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[[.,[.,.]],.]]],.],.]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[[.,[.,.]],[.,.]],[.,[[.,.],.]]],.]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[[[.,.],[.,.]],.]],.],.],.],.]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[[[.,[.,.]],.],.]],.],.],.],.]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[[[[.,.],.],.],[.,.]]]],.],.]
[1,0,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[.,.],[[.,.],.]],[.,.]],.],.],.]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[[[[.,[[.,.],.]],[[.,.],.]],.],.],.]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[[[[[.,[.,.]],.],[[.,.],.]],.],.],.]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0]=>[[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[[[.,.],.],.],.],[[.,.],.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[[.,.],.],[[[[.,[.,.]],.],.],.]],.]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[[[[[.,.],.],.],[[[.,.],.],.]],.],.]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[[[.,.],.],.],[[[.,[.,.]],.],.]],.]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,[[[[.,.],.],.],.]]],.],.]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[[[[.,.],[.,.]],[[[.,.],.],.]],.],.]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[[.,[.,.]],.],.],.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[[[.,.],.],.]],.]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,[.,.]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,[.,[.,.]]],[.,.]],[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,[.,[[.,.],.]]]],[.,.]],[.,.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[[.,.],.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[[.,[[.,.],.]],.],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[[[.,[.,.]],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[.,[.,[.,.]]],[.,[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[[.,.],[[[[.,.],.],.],.]],.],[.,.]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[[.,.],[.,[[[[.,.],.],.],.]]]],.]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[[[[.,.],.],.],.]]],.]],.]
[1,0,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[.,[[[[.,.],.],.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],[.,.]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,[[.,.],[.,.]]],.]],[.,.]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,[.,.]],[[.,.],[.,.]]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[[.,[.,.]],[.,.]],[.,.]]],.],.]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],[.,.]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[[[.,[[.,.],[.,[[.,.],[.,.]]]]],.],.]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[[.,[[.,.],[[[.,[[.,.],.]],.],.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[[[.,[[.,.],[[.,[[.,.],.]],.]]],.],.]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[[.,.],[.,[[.,.],.]]]],.],.],.]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[.,[[[.,.],.],[[.,[.,[.,.]]],.]]],.]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[.,[[[.,.],.],[.,[.,[.,.]]]]],.],.]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[.,[[[.,.],.],[[[.,[.,.]],.],.]]],.]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[.,[[[.,.],.],[[.,[.,.]],.]]],.],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[[[.,.],.],[.,[.,.]]]],.],.],.]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[[[[.,.],.],.],[[[.,.],.],.]]],.]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,[[[[.,.],.],.],[[.,.],.]]],.],.]
[1,1,0,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[[[.,[.,.]],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[.,[[.,.],.]],.],.],.],.]],.]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[[.,.],[.,.]],.],.],.],.]],.]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[[[[.,.],.],.],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],[[[[[.,.],.],.],.],[.,.]]],.]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,[[[.,.],.],.]],.],.],.],[.,.]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[[.,.],.],[.,[[[[.,[.,.]],.],.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[[[[.,.],.],.],.]],.],[.,.]],.]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[[.,[[[.,.],.],.]],.],[[.,.],.]],.]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[[[.,[[.,.],.]],.],[[[.,.],.],.]],.]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[[[[.,.],.],.],.]],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[[.,.],.],[[[[[.,.],.],.],.],.]],.]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[.,[[[.,.],.],.]],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[.,[[.,.],.]],.],.],[[[.,.],.],.]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[.,[[[.,.],.],.]],.]],.],.],.]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[[[[.,.],.],.],.]],.]],.],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[[[.,.],.],.],.],.]],.]],.]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,[[.,.],[.,.]]]]],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]],.]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[[.,.],[.,[[.,[[[[.,.],.],.],.]],.]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[[[[[.,.],.],.],.],[[.,[.,.]],.]],.]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[[[[[.,.],.],.],[.,[[.,.],.]]],.],.]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[[[[.,.],.],.],[.,[[.,[.,.]],.]]],.]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[[[.,.],.],.]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[[.,[.,.]],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[.,.],[[[[[[.,.],.],.],.],[.,.]],.]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[[.,.],[.,[[[.,[[[.,.],.],.]],.],.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]],.]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,[.,[.,.]]],[.,[.,.]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[[[.,.],.],.],.],.]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,[.,.]],.]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],.]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],.]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[[.,.],[.,.]],.]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,[[.,.],[.,.]]],[.,.]],.]]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,.],.],[[[[.,.],[.,.]],[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[[.,.],[.,.]]],[[[.,.],[.,.]],.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[[[[.,.],.],.],.],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[[[.,.],.],.],[.,[[[.,[.,.]],.],.]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],.],[[.,.],.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[.,[.,[.,.]]],.],.],.],[[.,.],.]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[.,[.,[[.,.],.]]],.],.],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[[.,.],[.,.]],.],.],.],.]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[[[.,.],.],.],.]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[[.,.],[.,.]],[.,[[[[.,.],.],.],.]]]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[[.,[[.,.],.]],.],[.,.]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[[[.,[.,.]],.],.],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[.,[.,[[.,.],.]]],.],.],[.,.]],.]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[[[.,.],.],[[.,.],[[.,.],.]]],.],.]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[.,[[[.,.],.],.]]],[.,.]],.],.]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[[.,[.,[.,.]]],.],.],.]],.],.]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,[[.,.],.]],.],[[[[.,.],.],.],.]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],[.,.]],[[[[[.,.],.],.],.],.]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[[[.,.],.],[.,.]],[[[[.,.],.],.],.]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[[[.,.],.],.],[.,.]],[[[.,.],.],.]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[[[[[.,.],.],.],.],[.,.]],[[.,.],.]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[[[[.,.],.],.],[[.,[.,.]],[.,.]]],.]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[[[.,.],.],[[.,.],[.,.]]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[[[[.,.],[.,.]],[[.,[.,.]],.]],.],.]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],[[.,[.,.]],[.,.]]],.],.],.]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[[.,.],[.,.]],.],[[[[.,.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[[.,.],[[[[[.,.],.],.],.],.]],.],.]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[[[.,.],[.,.]],.]],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[[[.,.],[.,.]],[.,.]]],.],.],.]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,.],[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[[[.,.],.],[[[.,.],.],.]],.],[.,.]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[[.,.],[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[[[.,[.,.]],.],.],.],.]]],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[[[[.,.],.],.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[[.,.],[[.,.],.]]],.],.],.],.]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[.,[[[.,.],.],.]],.],.],.]],.]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,[.,[[.,.],.]]]],.]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[[[.,.],.],[.,[.,[.,[[.,.],.]]]]],.]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,[.,[[.,.],.]]]]],.],.]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],[.,.]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[.,.],.],[[[.,[.,.]],[.,[.,.]]],.]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,[.,[[.,.],.]]]],[.,[[.,.],.]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[[[.,.],[.,.]],.],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[[.,.],.],[[[.,[.,.]],[.,.]],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],[.,.]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,[[[.,.],.],.]],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[[[.,[.,.]],.],.],.],.]],.],.]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[[.,.],[.,.]]]],.],.],.],.]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[[[.,.],.],[.,.]]]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[[[.,.],.],.],[[.,.],[.,.]]],[.,.]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[[.,.],.],.],[[.,[.,.]],.]],[.,.]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[[[.,.],.],[.,[[.,[.,.]],.]]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[[[.,.],.],[[[.,.],.],[.,.]]],[.,.]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[[.,.],.],[[.,[[.,.],.]],.]],[.,.]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[[[.,.],.],[[.,[.,[.,.]]],.]],[.,.]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[[[.,.],.],.],.],.]]],.]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[[.,.],.],[.,[[[[.,.],.],.],.]]],.]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[[.,.],[.,[[.,.],.]]],.]]],.]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[.,.],[[.,.],.]],.],[[.,.],.]],.]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[[.,.],.],[.,.]],.],[[.,.],.]],.]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[.,.],[[.,.],.]],.],.],[.,.]],.]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[.,[[[[.,.],.],.],.]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[[[.,[.,.]],.],.],.]]],.],.]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[[.,[[.,.],.]],[[.,.],.]],[.,[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,[.,[.,.]]],.]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,[.,.]],[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[[[.,.],.],[.,[[.,.],.]]],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[[.,[.,[.,.]]],.]]],[.,.]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,[[.,.],.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,[[[.,.],.],.]],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,[[[.,.],.],.]],[[[.,.],.],.]],.]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[[[.,.],.],.],.]],.]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,[[[[.,.],.],.],.]],[.,[.,.]]],.]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,[[[.,.],.],.]],[[.,[.,.]],.]],.]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[[.,[.,.]],.],.]],.]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[[.,[.,.]],.],.],.]],.]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[[.,[.,.]],.],.],.],.]],.]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,[[[.,.],.],.]],[.,[[.,.],.]]],.]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[.,[[.,.],.]],.]],.]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[[[.,.],.],.]],[.,[.,[.,.]]]],.]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[.,[[.,.],.]],.],.]],.]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[.,[.,[.,.]]],.]],.]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[.,[[.,.],.]],.],.],.]],.]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[.,[.,[.,.]]],.],.]],.]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[.,[.,[.,.]]],.],.],.]],.]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[[[.,.],[.,.]],.]]],[.,.]],.]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[[[.,.],[.,.]],[.,.]],.]]],.]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[[[.,.],.],.],[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[[.,[.,.]],.],[.,.]],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[[[.,.],.],.],.],[.,.]]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[[[.,.],.],[.,.]],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[[[.,.],[.,[[[[.,.],.],.],[.,.]]]],.]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[[.,[.,[.,[.,.]]]],[[.,[.,[.,.]]],.]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[.,[[.,.],.]]],.],.],.],.]
[1,1,0,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[.,[[.,.],.]],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]],.]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],[[.,.],[.,.]]]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[[.,.],[[.,.],.]],.]],[.,.]],.]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[[[[.,.],.],.],.]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[[[[.,.],.],.],.]]],.],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[[.,[[.,.],.]],.],.],.]],.],.]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[[[.,.],.],[[[.,.],.],.]],.]],.]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[[[[.,.],.],.],[.,.]],.],.]],.]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[[.,[.,.]],[[[[.,.],.],.],.]],.],.]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]],.]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]],.]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[[.,.],[[.,.],.]],[.,[.,[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]],.]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[[.,.],[.,[[.,.],.]]],[.,[.,.]]],.]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,[.,[[.,.],.]]]],[.,.]],.]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[[[[.,.],.],.],.]],[[[.,.],.],.]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[[[[.,.],.],.],.]]],[.,.]],.]
[1,0,1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[.,[[[.,[.,.]],.],[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,[.,[.,.]]],.],[[[[.,.],.],.],.]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[[.,.],[.,.]],.],.],[[[.,.],.],.]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[[.,.],[.,.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],.]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[[[.,.],[.,.]],.]],[.,.]]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[[[.,.],[.,.]],.]]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[[.,.],[.,.]],.],.]],.]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,[[.,[.,.]],.]],[[.,.],[.,.]]],.]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,[[[.,[.,.]],.],[.,.]]],[.,.]],.]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[.,.],.],[[[[.,.],.],.],[[.,.],.]]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[.,.],[[[.,.],[.,[.,[[.,.],.]]]],.]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.],.]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[[[.,[.,.]],.],.],.],.]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[[[.,.],[.,.]],.],.],.]],.],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[[.,.],[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,.],[[.,[.,.]],.]],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[[[[.,.],.],.],[.,.]],.]],.],.]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[[[.,.],.],[.,.]],.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[[[.,.],.],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[[.,.],[.,[[.,[.,.]],[[[.,.],.],.]]]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[[.,.],[.,[[.,[[[.,[.,.]],.],.]],.]]]
[1,0,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[.,[.,.]]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[[[[.,.],.],.],.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[.,.],[[.,.],[[[[.,.],.],.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[[.,.],[[.,[[[[.,[.,.]],.],.],.]],.]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[[.,[.,.]],[[[[.,.],.],.],.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]],.]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,[[.,[.,.]],.]]],[.,.]],[.,.]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],[.,[[.,.],.]]],[.,.]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[.,[[[.,.],.],.]],.]]],.],.]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[.,[[[.,.],.],.]],.],.]]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]
[1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[.,[[.,.],.]],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[[.,.],[[.,.],.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[[.,[.,.]],[.,.]],.],[.,.]]],.]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[.,[[.,[.,.]],.]],.],[.,.]]],.]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,[[.,.],.]],[.,.]],[.,.]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,[.,.]],.],[.,.]]],.]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[[[.,.],[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,[[.,.],[.,.]]],.]],.]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[[[.,.],[.,.]],[.,.]],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[.,.],[[[.,.],[.,.]],.]],[.,.]],.]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,.],[[.,.],.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],[[.,[.,.]],.]]],[.,.]]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[.,.],[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[.,.],[[[[[.,.],[.,.]],[.,.]],.],.]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],[[[.,.],[.,.]],.]],[.,[.,.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[[.,.],[[.,.],.]],[[.,[.,.]],.]],.]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[[.,.],.],[[.,[.,.]],.]],[.,.]],.]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,[.,.]],[.,.]],.]]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[.,.],[[.,.],[[.,[[.,.],[.,.]]],.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[[[[.,.],.],.],.]],[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[[.,[[.,.],[[[[.,.],.],.],[.,.]]]],.]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[[.,[.,.]],.],.],.]],.]],.]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[[[[.,.],.],.],.]]],.]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,[[[.,.],.],.]]]],.],.],.]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],[[.,.],.]],.]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[[[.,.],.],[[[.,.],.],[.,.]]],.],.]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[[[.,.],.],[[.,.],.]],.],.],[.,.]]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,[[.,.],.]],.]]],.]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[[[.,[.,.]],.],[[[.,.],.],.]]],.]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,[.,.]]],[[[.,.],.],.]]],.]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,[.,.]],[.,[[.,.],.]]]],.],.]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,[[[.,[.,.]],.],[[.,.],.]]],.],.]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,[[.,[.,[.,.]]],[[.,.],.]]],.],.]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.],.]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[[.,[.,[.,.]]],.],.]],.],.],.]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[[[[.,.],.],.],.]],.],.]],.]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[[[.,.],.],.],.]],.]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[.,[[.,.],.]],.],.],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[[.,[.,.]],.],.],.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,.],[[.,[.,.]],.]]],.]],.]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[.,[[.,.],[.,.]]],[.,.]],.]],.]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,[[.,.],.]],[.,.]]],[.,.]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[[[.,.],.],.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[[.,.],[[.,.],.]],.],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[[[.,.],[.,.]],.],.],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[[.,[.,[[.,.],[[[.,.],.],[.,.]]]]],.]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[.,[[[.,.],.],.]],[.,.]]]],.]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[[[.,.],.],[.,[.,[[.,.],.]]]],.],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,[[[.,.],.],.]]],[.,.]],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]],.]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,[[.,.],[.,.]]],[[.,.],[.,.]]],.]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[[[.,.],.],.],.]],.]],.]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[[[.,.],.],.]],[.,.]],[.,.]],.]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[[[[.,[.,.]],.],.],.],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,[[.,.],.]]],[[[[.,.],.],.],.]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,[.,.]],[.,.]]],.]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],[.,.]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],[[[.,.],.],.]],[.,.]],[.,.]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,[[.,.],[.,.]]],.]]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,[[[.,.],.],.]]],.]],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[[[.,.],.],.],.]],[.,.]],[.,.]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,[[.,.],.]],.],[.,.]],[.,.]],.]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[[[.,[.,.]],.],.]],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[[.,[.,[.,.]]],.],.],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,[.,[.,[.,.]]]],.],[.,[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[[.,.],[.,.]],.],[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[[[.,.],[.,.]],[.,.]]],[[.,.],.]]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[[[.,.],.],[.,[[.,.],.]]],.]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[.,.],[[[.,.],[.,[[[.,.],.],.]]],.]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[.,[.,.]],[.,[.,[[[.,[.,.]],.],.]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[[.,[.,.]],.],.],.],.]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,[.,[.,.]]],.],.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[.,[[.,[.,.]],.]]],.],.]],.]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[[.,[.,[.,.]]],.]],.],.]],.]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[.,[.,[.,[.,.]]]],.],.],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[.,[[.,[.,.]],.]],.]]],.],.]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[[.,[.,[.,.]]],.],.]]],.],.]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[.,[[.,[.,.]],.]]],.]],.],.]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[[.,[.,[.,.]]],.]],.]],.],.]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,[[.,[.,.]],.]]]],.],.],.]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[[.,[.,[.,.]]],.]]],.],.],.]
[1,0,1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[[[.,.],.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[[.,.],[[.,.],.]]]],.]],.]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[[[.,[[.,.],.]],[[[.,.],.],.]],.],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[[.,.],.],[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[[[.,.],.],.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],[.,[.,[.,.]]]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[[.,.],[.,[.,.]]],.],.]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],[.,[.,.]]],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,[.,[.,[.,.]]]],.],.]]
[1,1,0,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,[.,[[.,.],.]]],[.,[[[.,.],.],.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[[[[[.,.],.],.],[.,.]],.],[[.,.],.]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]],.]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,[.,[[.,.],.]]],.]],[.,.]],.]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[.,[[.,[.,.]],.]],.]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[[.,.],.],[[.,[[.,[.,.]],.]],.]],.]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[[.,[[.,.],[[.,[[.,[.,.]],.]],.]]],.]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[.,[[.,.],.]]],.]],[[.,.],.]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[[.,[.,[.,.]]],.]],[[[.,.],.],.]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[[.,.],.],[.,.]]],[.,.]],[.,.]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,[.,[.,.]]],.]],[.,.]],[.,.]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[[[.,.],.],[.,.]]]],.],.]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],[.,[[.,.],[.,.]]]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[[[.,.],.],.],[[[.,.],.],[[.,.],.]]]
[1,0,1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[[.,.],.],[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[.,.],[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]],.]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,[.,.]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[[.,.],[.,[.,.]]],[.,.]]],.],.]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],.]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,[.,[[.,.],.]]],[.,[.,.]]],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[.,[.,[.,.]]],.],.],[[.,.],.]],.]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[[.,.],.],[[[[.,.],.],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[[[.,.],.],[.,.]]],[[.,.],.]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[[[[.,.],.],.],[.,[[[.,.],.],.]]],.]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],[[.,[.,.]],[.,.]]],.]],.]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,[[.,[.,.]],.]],[.,.]]],.]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[[.,.],[.,.]],.]],[.,.]],.],.]
[1,1,1,1,0,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[.,[.,[.,.]]],[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,.],[[[[.,.],.],.],.]]],.]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[[.,.],.],[.,.]],.],.],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[[[.,.],.],.],.]],[[.,[.,.]],.]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],[[[[.,.],.],.],.]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[[.,.],[[[.,.],.],.]],.],[.,[.,.]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[[.,.],[[.,[.,[[[.,.],.],.]]],[.,.]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[.,.],[[.,.],.]],.],.],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[.,[[.,.],.]]],[[.,.],[.,.]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[[.,.],[.,[.,.]]],.],[[.,.],[.,.]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],[.,[.,[[.,.],.]]]],.]],.]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[[[.,.],[.,.]],.]],.],[.,.]],.]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[.,[[[.,.],.],[.,[[.,.],.]]]],.],.]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[[.,.],[.,[[[.,[[.,.],[.,.]]],.],.]]]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[[.,[[.,.],.]],.],.],.]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]],.]
[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]=>[[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]],.]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]],.]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]],.]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]
[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]=>[[.,.],[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]],.]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]],.]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]],.]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[[.,.],[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]
[1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]],.]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]],.]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]],.]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]],.]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[[.,.],[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]
[1,0,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[.,.],[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]],.]
[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]=>[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[.,.],[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[[[[[[.,.],.],.],.],.],.],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[[[.,[.,.]],.],.],.],.],.],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[[[[[.,.],.],.],.],.],.],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[[[[[.,.],.],.],.],.],[[.,[[.,.],.]],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[[[[.,.],.],.],.],[[[.,[[.,.],.]],.],.]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[[[.,.],.],.],[[[[.,[[.,.],.]],.],.],.]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[[[[.,[[.,.],.]],.],.],.],.]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[[.,[[.,.],.]],.],.],.],.],.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[[[[[.,.],.],.],.],.],[.,[[[.,.],.],.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[[[[[.,.],.],.],.],.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[[[[[.,.],.],.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,[[[.,.],.],.]],.],.],.],.],.]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[[[[.,.],.],.],.],[.,[[[[.,.],.],.],.]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[[[[.,.],.],.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[[[.,.],.],[.,.]]],.],.],.],.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[.,[[[.,.],.],.]]],.],.],.],.]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[[.,.],.],.],[.,[[[[[.,.],.],.],.],.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[[.,.],.],.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[[[[[.,.],.],.],.],.]],.],.],.]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[[[[.,.],.],.],[.,.]]],.],.],.]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[.,[[[[.,.],.],.],.]]],.],.],.]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[.,.],.],[.,[[[[[[.,.],.],.],.],.],.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[.,.],.],[.,[[[[[.,.],.],.],.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[[[[.,.],.],.],.],[.,.]]],.],.]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[.,.],.],[[.,[[.,.],[[.,[.,.]],.]]],.]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[[[[[.,.],.],.],.],.]]],.],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[[[[[.,.],.],.],.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[[[[[.,.],.],.],.],.],[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[[[[.,.],.],.],[.,[.,.]]]],.],.]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[[[[.,.],.],.],.],.]]],.]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[[[[.,.],.],.],.],.],.]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[[[[[.,.],.],.],.],.],.]]],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[[[.,.],.],.],.],[.,.]],[.,.]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],.],.],[.,[.,.]]],.],.],.]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[.,.],.],.],[.,.]],.],.],.],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],.],[.,.]],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[[[.,.],.],.],[.,.]],[.,.]],[.,.]],.]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],.],[.,[.,.]]],.],.],.],.]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[[[[.,.],.],.],[.,[.,[.,.]]]],[.,.]],.]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],[.,.]],[.,.]],.],.],.],.]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[[.,.],.],[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],[.,[.,.]]],.],.],.],.],.]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],.],[.,[.,[.,.]]]],.],.],.],.]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[[[[[[.,.],.],[.,[.,[.,[.,.]]]]],.],.],.]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[[[[[.,.],[.,.]],.],[.,[.,.]]],.],[.,.]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[[.,.],[.,.]],[.,.]],[.,.]],.],.],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[[.,.],[.,.]],[.,[.,.]]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[[[.,.],[.,.]],[.,[.,[.,.]]]],.],.],.]
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.],.]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[.,.],[.,[.,.]]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],[.,[.,[.,.]]]],.],.],.],.],.]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.],.]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[[[.,[.,.]],.],.],.],.],[.,[.,.]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[[[.,[.,.]],.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[[[.,[.,.]],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,[.,.]],.],[.,.]],.],.],.],.],.]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[[[.,[.,.]],.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.],.]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[[.,[.,.]],[.,.]],.],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[.,.]],[.,.]],[.,.]],.],.],.],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[[[[[.,[.,.]],[.,.]],[.,.]],.],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[[.,[.,.]],[.,.]],[.,[.,.]]],.],.],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[.,.]],[.,[.,.]]],.],.],.],.],.]
[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]=>[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]
[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]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[.,[[[[[.,.],.],.],.],[[[.,[.,.]],.],.]]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[.,[[[[.,.],.],.],[[[[.,[.,.]],.],.],.]]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[[.,.],.],[[[[[.,[.,.]],.],.],.],.]]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]],.]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]],.]
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]]
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[.,[[.,.],.]],.],.],.],.],.],[.,.]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[.,[.,[.,.]]],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,[.,[.,.]]]],[.,[[[[.,.],.],.],.]]]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]]
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[[.,.],[.,[.,[[[[[.,.],.],.],.],.]]]]]
[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[[[[.,.],.],.],.]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]]
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[.,[.,[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[.,[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],.],[.,[.,[.,.]]]],.],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[[[[[.,.],.],.],.],.]],[[[.,.],.],.]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[[.,.],[.,[[[.,.],.],.]]],.],.],.]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],.],[.,[[.,.],.]]],.],.],.]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[[[[.,.],.],.],[.,[.,.]]],.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[[.,.],[[[[[[.,.],.],.],.],.],.]],.],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[.,.],.],[[.,.],.]],.],.],.],[.,.]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[.,.],[[[.,.],.],.]],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,[[[[.,.],.],.],.]],.],.],.],[.,.]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]]]
[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[[[[.,.],.],.],.],[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[.,[.,[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[.,[[[[.,.],.],.],.]],.],.],.]],.]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[.,.],[[[.,.],.],.]],.],.],.]],.]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[[.,.],.],[[.,.],.]],.],.],.]],.]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[[[.,.],.],.],[.,.]],.],.],.]],.]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[[[[.,.],.],.],.]],.]]]]]
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[[.,.],[.,[[[[[.,.],.],.],.],.]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,[[[.,.],.],.]],.],.]]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[[.,[[.,.],.]],.],.],.]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[[[[[.,.],.],.],.],.],.]]],.],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[[[[[.,.],.],.],.],.]]],.],.],.]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[[[[.,.],.],.],.]]],.],.],.],.]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,[[[.,.],.],.]]],.],.],.],.],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[[[[[.,.],.],.],.],.],.],.]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[[[[[.,.],.],.],.],.]]]],.],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[[[[[.,.],.],.],.],.]],.],.]]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[[[[.,.],.],.],.],[[.,.],.]]]]]
[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],.]],.]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,[[.,.],.]]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[[[[[.,.],.],.],.],.]],.]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[.,[[[[.,.],.],.],.]]],.]]]]
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[[[[.,.],.],.],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],.],[[.,.],.]],.],.],.],.]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],[[.,.],.]],.],.],.],.],.],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[[[[.,.],.],.],.]],.],.],.],.]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],.],[[[.,.],.],.]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[[[.,.],.],.],[[.,.],.]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[[[[[.,.],.],.],.],.]]]],.]]
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,.],.],[[[.,.],.],.]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[[[[[.,.],.],.],.],.]]],.]]]
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[.,.]],[[.,.],.]],.],.],.],.],.]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[[[.,[.,.]],.],.],.],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],.]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[[[.,.],.],.],[[[[.,[.,.]],.],.],.]],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[[.,.],.],[[[[[.,[.,.]],.],.],.],.]],.]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[.,[[.,[.,[.,.]]],[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[[.,.],.],[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[[[[.,.],.],.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[[[[[.,.],.],.],[.,.]],[[.,.],.]],.],.]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],[.,.]]
[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]=>[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,[[[.,[.,.]],[.,.]],[.,.]]],[.,.]],.]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[[.,[.,.]],[.,.]]],[.,.]],[.,.]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]],.]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],.],[[.,.],[.,.]]],.],.],.],.]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[[[.,.],.],[.,.]]],.],.],.],.]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[[[[.,.],.],.],[.,.]]],.],.],.],.]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0]=>[.,[[.,.],[.,[[[[.,[.,[.,.]]],.],.],.]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[.,[[[.,.],.],[[[[.,[.,[.,.]]],.],.],.]]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[[[.,.],.],[.,[.,[.,.]]]],.],.]]]
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[[[[.,.],.],.],[.,[.,.]]]]],.]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[[[[[.,.],.],.],.],[.,.]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[[[[[.,.],.],.],.],.]],.],[.,.]],.]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[[.,[[[[.,.],.],.],.]],.],[[.,.],.]],.]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[[[.,[[[.,.],.],.]],.],[[[.,.],.],.]],.]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[[[.,[[.,.],.]],.],[[[[.,.],.],.],.]],.]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[[[[[.,.],.],.],.],.]],.]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.],.]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[.,[.,[.,[[.,.],.]]]],.],.]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]]]
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]]]
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]]
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[.,[.,.]],[[[[.,.],.],.],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]],.]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[[[[.,.],.],.],.],.],.]]]
[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[[.,[[.,.],.]],.],.],.],.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]]
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[.,[.,[.,[.,.]]]],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,[[.,[.,.]],.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[.,[.,[.,.]]],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]]]
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]]]
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]]
[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]=>[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[[[.,.],[.,.]],[.,.]],[.,.]],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[[[.,.],[.,.]],[.,.]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],.]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[.,[.,[[.,.],.]]]],.],.],.],.]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],.],[.,[[.,.],.]]],.],.],.],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.],.]
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[[.,[.,[.,.]]],.],.],.],.]]]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[[[.,.],[.,.]],.],.],.],.]]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[[.,[[.,.],.]],[[[[.,.],.],.],.]]]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[.,[[.,[.,[[.,.],.]]],[.,[[[.,.],.],.]]]]
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]]]
[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[.,[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[.,[[[[[[.,.],.],.],[.,[.,.]]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],[.,.]],[.,[.,.]]],.],.],.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]],.]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[[.,[.,.]],.]],.],.],.],.],.],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.],.]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[[[.,.],[.,.]],[.,.]],[.,.]],.],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[[.,.],[.,.]],[.,.]],.],[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[[[.,.],[.,.]],.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]],.]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]],.]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]],.]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[.,[.,[[[[[.,.],.],.],.],[[[.,.],.],.]]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[.,[.,[[[[[.,.],.],.],.],[.,[[.,.],.]]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[[.,.],[.,.]],[[[.,[.,.]],[.,.]],[.,.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[[[.,[.,.]],.],.],.],[[[[.,.],.],.],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[[[[.,.],.],.],.],[[.,.],[.,.]]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[[[.,.],.],.],.],[[.,[.,.]],.]],[.,.]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[[[[.,.],.],.],[[.,.],[.,.]]],[.,.]],.]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[[[.,.],.],.],[[.,[.,.]],.]],[.,.]],.]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[.,[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[[[[.,.],.],.],.],.],.]]],.]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[[.,.],.],[.,[[[[[.,.],.],.],.],.]]],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[[.,[.,[.,.]]],.],.],.],[[.,.],.]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]]
[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]=>[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]],.]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[[[[.,.],.],.],.],.]],[[.,.],.]],.]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,[[[[.,.],.],.],.]],[[[.,.],.],.]],.]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,[[[.,.],.],.]],[[[[.,.],.],.],.]],.]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[[[[.,.],.],.],.],.]],.]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,[[[[[.,.],.],.],.],.]],[.,[.,.]]],.]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,[[[[.,.],.],.],.]],[[.,[.,.]],.]],.]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,[[[.,.],.],.]],[[[.,[.,.]],.],.]],.]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[[[.,[.,.]],.],.],.]],.]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[[[.,[.,.]],.],.],.],.]],.]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]],.]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[[[[.,.],.],.],.],[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[[[.,[.,.]],.],.],[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],[.,.]]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[[.,.],[[[[.,.],.],.],.]],.]]]]
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[[[.,.],.],[[[.,.],.],.]]],.]]]
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[[[[.,.],.],.],[[.,.],.]]]],.]]
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[[[.,.],.],[.,[[.,.],.]]]],.]]]
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[[.,.],[.,[[[.,.],.],.]]],.]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[[.,[.,[.,[.,.]]]],.]],.],.],.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[[.,[.,[.,.]]],.]],.],.],.],.]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,[[.,[.,.]],.]],.],.],.],.],.]]
[1,1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[[[[[.,.],.],.],.],.],.]]],[.,.]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[[[[.,.],.],.],.]]]]],.]]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[.,[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[[[[.,[.,.]],.],.],.],.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[.,.],[[.,.],.]],[.,.]],[.,.]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]],.]
[1,1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[[[.,[.,.]],.],.]]]]]]
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[.,[[.,.],[.,[.,[[[[.,[.,.]],.],.],.]]]]]
[1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[[.,.],[.,[[[[[.,[.,.]],.],.],.],.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[[[[.,[.,.]],.],.],.],.],.]],[.,.]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[[.,.],[[.,.],[[.,.],.]]]]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[[[.,.],[.,.]],.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[.,.],[[[.,.],[.,[[.,.],[[.,.],.]]]],.]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,[[.,.],[[.,.],.]]]],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[[.,.],[[[[.,.],[.,.]],.],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[[.,.],[[[.,[.,.]],.],[.,[[.,.],.]]]],.]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[[.,.],[.,[[.,.],.]]]],.],[.,.]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],[.,[.,[[.,.],.]]]],.],[.,.]],.]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,.],[.,[[.,.],.]]],.]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[.,.],[.,[[.,.],.]]],.]]],.]
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[[[.,.],[.,.]],.],[[.,[.,[[.,.],.]]],.]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,[.,[[.,.],.]]],.]],.]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,[.,[[.,.],.]]],.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[[.,.],[[.,.],[[[[.,.],[.,.]],.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[[[.,.],[.,[[[[.,.],[.,.]],.],[.,.]]]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[[[.,.],[.,.]],.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[[.,.],[[[.,[.,.]],.],[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[[.,[.,.]],.],[.,.]]],.]],.]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[[.,.],[[.,.],[.,.]]],.],[[.,.],[.,.]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[[[[.,.],[.,[.,.]]],.],[[.,.],[.,.]]],.]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[[.,.],[[[.,.],[.,.]],.]],.],[.,[.,.]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[.,.],[[.,[.,.]],.]],.],[.,[.,.]]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[[.,.],[[.,.],[.,.]]],.],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],[[[.,[[.,.],[.,.]]],.],[.,.]]],.]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[[.,.],[[[[[.,.],[.,[.,.]]],.],[.,.]],.]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[[[.,[.,[.,.]]],.],[.,.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[[[.,.],[.,[[.,.],[[[.,.],[.,.]],.]]]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[[[.,.],[.,.]],.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[[.,.],[[[.,.],[.,[[[.,.],[.,.]],.]]],.]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,[[[.,.],[.,.]],.]]],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[.,.],[[[[.,.],[.,.]],.],[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[[.,.],[[[.,[.,.]],.],[[.,[.,.]],.]]],.]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[[.,.],[[.,[.,.]],.]]],.],[.,.]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],[.,[[.,[.,.]],.]]],.],[.,.]],.]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,.],[[.,[.,.]],.]],.]]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[.,.],[[.,[.,.]],.]],.]]],.]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[[.,.],[.,.]],.],[[.,[[.,[.,.]],.]],.]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,[[.,[.,.]],.]],.]],.]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[[[[.,.],.],.],.],.]],.]]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[.,[[[.,.],.],[[[.,[[[.,.],.],.]],.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[[[[.,.],.],[.,.]],.],[[[.,.],.],.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[[[.,.],[.,.]],.],.],.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[[.,.],.],.]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[[[[.,.],.],.],.]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,.]]]],[[[[[.,.],.],.],.],.]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[[[.,.],[.,.]],.],.],.],.],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[[[[.,.],.],.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[[[.,[.,.]],[.,.]],[[[.,.],[.,.]],.]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],[[[.,.],[.,.]],.]],[.,.]],.]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[.,[[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]],.]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]],.],.]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[[[.,.],.],[.,[.,[.,[.,[[.,.],.]]]]]],.]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]
[1,0,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[.,[[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]]
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]]
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,[[.,.],[.,.]]],.]],[.,.]],[.,.]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[[[.,.],.],[.,.]],.],.]]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[.,[[[.,[[[.,[.,.]],.],.]],[.,[.,.]]],.]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[[[[.,.],.],[.,.]],.],.]]],[.,.]]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[.,.],[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[.,[[[[[.,.],.],.],.],.]],.],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[[[[[.,.],.],.],.],.]],.],.],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,[[[.,.],.],.]]]],.],.],.],.]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[[[[[.,.],.],.],.],[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[[[[.,[.,.]],.],.],.],.],.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,.],[[.,[.,.]],.]],[.,.]],[.,.]],.]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,.],[[.,.],[.,.]]]],[[.,.],.]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[[.,.],[[.,.],[.,.]]]],.]],.],.]
[1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[.,[[.,.],[[.,[[.,.],[.,.]]],[[.,.],.]]]]
[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]=>[[[.,.],[[.,[[.,[[.,.],[.,.]]],.]],.]],.]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[.,[[.,.],.]],[.,.]]],[[.,.],.]],.]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[[.,[[.,.],.]],[.,.]]],.],[[.,.],.]]
[1,1,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,[.,.]],[[.,.],.]]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[.,[[.,.],.]],[[.,[.,.]],[[.,.],.]]],.]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,.],[[.,.],[[.,[.,.]],.]]]],.],.]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,.],[[.,[.,.]],.]]],.]],.]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],[[.,.],.]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,[[.,[.,.]],.]],.]]],.]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,.],.],[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[.,.],[.,[[.,.],.]]]],[[.,.],.]],.]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[[.,.],[.,[[.,.],.]]]],.],[[.,.],.]]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,[.,[[.,.],.]]],[[.,.],.]]],.]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,[.,[[.,.],.]]],.]],[[.,.],.]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,[.,[[.,.],.]]],.]],.]],.]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],[.,[[.,.],.]]]]]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[[.,[[.,.],.]],[[.,.],[.,[[.,.],.]]]],.]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[[[.,.],[[.,[[.,.],.]],[.,[[.,.],.]]]],.]
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[[.,[[.,.],.]],.],[[.,[.,[[.,.],.]]],.]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[[.,.],[[.,.],.]],[[.,[.,[[.,.],.]]],.]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[[[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],.],.]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,.],[[.,.],[.,.]]]],.]],.]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,[[.,.],.]],[[.,.],[.,.]]],[[.,.],.]]
[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]=>[[[.,.],.],[[.,[[.,[[.,.],[.,.]]],.]],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,[[.,.],.]],[.,.]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,[[.,.],.]],[.,.]]],.]],.]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[[.,[[.,.],.]],.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[[.,.],[[.,.],.]],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]],.]
[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]=>[.,[[.,[[.,.],.]],[[.,[[.,[.,.]],.]],.]]]
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[[[[.,.],.],.],[.,[[[.,.],.],.]]]]]
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[[[.,.],.],[.,[[[[.,.],.],.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[.,[[.,[[[[[.,.],.],.],.],.]],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,[[[[.,.],.],.],.]],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[.,[[.,[[[.,.],.],.]],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[.,[[.,[[.,.],.]],[.,[.,[[[.,.],.],.]]]]]
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[[.,[.,.]],[.,[.,[[[[.,.],.],.],.]]]]]
[1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,.],[[.,[.,.]],.]]],.]]]
[1,1,0,1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[.,[[.,.],[.,[[[.,.],[.,.]],[[.,.],.]]]]]
[1,1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[.,[[.,.],[[[.,[.,.]],[.,[.,[.,.]]]],.]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[.,[[.,.],[.,[[[.,.],[[.,.],.]],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[.,[[.,.],[[.,[.,.]],[.,[[.,.],[.,.]]]]]]
[1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[.,.],[[[.,.],[[[.,.],.],[.,.]]],.]]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[.,[[.,.],[[[.,.],[[.,.],.]],[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[[.,[.,[.,.]]],[[.,.],.]],.]]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[[.,.],[[[.,[.,.]],.],.]],.]]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0,0]=>[.,[[.,.],[[.,[.,[[.,[.,.]],.]]],[.,.]]]]
[1,1,0,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,0]=>[.,[[.,.],[.,[[[.,[.,.]],[[.,.],.]],.]]]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[.,[[.,.],[[[.,.],[.,[.,[.,.]]]],[.,.]]]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0,0]=>[.,[[.,.],[.,[[[.,[[.,.],.]],[.,.]],.]]]]
[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,[[.,.],[.,.]]],.]]]]
[1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[[.,[.,.]],.],[[.,[[.,.],[.,.]]],.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[.,[[[.,[.,.]],.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[.,[[[.,[.,.]],.],[[[.,.],[[.,.],.]],.]]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[.,[[[.,[.,.]],.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[.,[[[.,[.,.]],.],[[.,.],[[.,[.,.]],.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,[[.,[.,.]],.]],.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[.,[.,.]],[.,[.,.]]]],.],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[[.,.],[[.,.],.]],.]],.],[.,.]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[.,[.,[.,.]]],[.,.]]],.],[.,.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[.,.],[[.,[.,.]],.]]],.],[.,.]]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,.],[[.,[.,.]],.]]],.]],.]]
[1,1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[[[.,.],[.,.]],[[.,.],.]]]],.]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]],.]]
[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[[[.,.],[[.,.],.]],[.,.]]]],.]]
[1,1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]],.]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,.],[[[.,.],.],[.,.]]],.]],.]]
[1,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[[.,.],[[.,.],.]],[.,[.,.]]]],.]]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[.,[.,.]]],[[.,.],.]],.]],.]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,.],[[[.,[.,.]],.],.]],.]],.]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]],.]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[[.,[.,.]],[[.,.],.]],.]]],.]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[[.,[[.,.],.]],[.,.]],.]]],.]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,[[.,.],[.,.]]],.]]],.]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[.,.],[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[.,.],[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[[[.,[.,.]],.],.],[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[[[.,[.,.]],.],[.,.]],.],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[[[.,[.,.]],.],[[.,.],[.,.]]],.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[[.,[[[.,.],[.,.]],.]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[.,[.,.]],[[.,.],.]],.],[.,.]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[.,[[.,[.,[.,.]]],[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]],.]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]],.]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[[[.,.],[.,.]],[.,.]],.]],[.,.]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],[[[.,.],[.,.]],.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[[.,.],[[.,[.,.]],.]]],[.,.]],.]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]],.]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[.,[[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[[[[[[.,.],.],.],.],.],.]],[[.,.],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[.,[.,.]],[[.,.],[[.,[[[.,.],.],.]],.]]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,.],[[[.,.],.],.]]],.]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,[[[.,.],.],.]],.]],.]]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[.,[[[[.,[.,.]],.],[.,.]],[[[.,.],.],.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],.],[[[.,[.,.]],.],.]],.]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[.,[[[[.,[.,.]],[[[.,.],.],[.,.]]],.],.]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[.,[[[.,[.,.]],.],.]],[.,.]],.],.]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,.],[[[.,.],.],.]]]],.]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,[[[.,.],.],.]],.]]],.]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[[[.,[.,.]],.],[.,.]],.],.]]],.]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[.,.]],[[[.,.],.],.]]],.]],.]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[[.,[.,.]],.],.]],.]],.]],.]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[[[.,.],.],[.,.]],[[.,.],[[[.,.],.],.]]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[[[.,.],.],[.,.]],[[.,[[[.,.],.],.]],.]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[[[.,.],.],[[[[[.,[.,.]],.],[.,.]],.],.]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[[[[.,.],.],[[.,[.,.]],[[[.,.],.],.]]],.]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[[[[.,.],.],[[.,[[[.,[.,.]],.],.]],.]],.]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],[[[.,.],.],[.,.]]],[[[.,.],.],.]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[[.,.],.],[.,[.,.]]],.],.]],.]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[.,[[[.,.],.],.]],[.,.]],[[[.,.],.],.]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],[[.,.],[[[.,.],.],[.,.]]]],.],.]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[[.,.],[[.,[[[.,.],.],.]],[.,.]]],.],.]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[[[[.,.],.],[.,.]],.],[.,.]]],.],.]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[.,.],[[[.,.],.],.]]],[.,.]],.],.]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[.,[[[.,.],.],.]],.]],[.,.]],.],.]
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[[.,.],.],[.,.]]]]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[[.,.],[[.,.],[[.,[[[.,.],.],.]],[.,.]]]]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[[[[.,.],.],[.,.]],.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[[.,.],[[.,[[.,.],[[[.,.],.],.]]],[.,.]]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[[.,[[[.,.],.],.]],.]],[.,.]]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[.,[[[[.,.],.],[.,.]],[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[.,[[[[.,.],.],[[[.,[.,.]],.],.]],[.,.]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[[.,.],[[[.,.],.],[.,.]]],.],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[[[.,[[[.,.],.],.]],[.,.]],.],[.,.]]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[[.,[[.,.],[[.,.],[[[.,.],.],.]]]],[.,.]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[[.,[[[.,.],.],.]],.]]],[.,.]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,.],[[[.,.],.],.]]],.]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,[[[.,.],.],.]],.]],.]],[.,.]]
[1,1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[[.,.],[.,[.,[.,.]]]]]],[.,.]]]
[1,1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[.,[[.,[.,[.,.]]],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[.,[[.,[.,[.,[[.,.],[.,.]]]]],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[[[[[[.,.],.],.],.],.],[[.,.],.]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[[[[.,.],.],.],.],.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[.,[[[[.,.],.],.],.]],.],.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,.]],[[[.,.],.],.]],.],.],.],.]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],[.,.]],[[.,.],.]],.],.],.],.]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[[.,.],[.,.]],[.,.]],.]],.]],.]
[1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]]]
[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,.],[[.,[.,.]],.]]],.]],[.,.]]
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[[[[.,.],.],.],[.,[[.,.],.]]]]]]
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[[[.,.],.],[.,[[[.,.],.],.]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[.,[[[[.,.],.],.],.]]],[[.,.],.]]]
[1,1,1,1,0,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,[.,[[[.,.],.],.]]],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[.,[[.,[.,.]],[.,[.,[.,[[[.,.],.],.]]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]],.]
[1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]],.]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[[[[.,.],.],.],.]],.]]]],.]
[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]=>[[.,.],[.,[.,[[.,[[[[.,.],.],.],.]],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[[[[.,.],.],.],.],.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[[[.,.],.],.]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[[[[[.,.],.],.],.],[.,.]],.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[.,[.,[[[[[[.,.],.],.],.],[[.,.],.]],.]]]
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[[[[.,.],.],.],.],[.,[.,.]]],.]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[[[[[.,.],.],.],.],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[.,[[[[.,.],.],.],.]],.],.],[.,.]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[.,[[[.,.],.],.]],.],.],.]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,[.,.]],[[.,.],.]],.],.],.],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[[.,[.,.]],[.,[[.,.],[[[.,[.,.]],.],.]]]]
[1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[.,[[[.,.],.],[.,.]]],.]]]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[[[[.,.],.],.],.]]]]]
[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]=>[[.,[.,[[.,[[[.,.],.],[.,.]]],.]]],[.,.]]
[1,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[.,[[[.,[[.,.],.]],.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[[.,[.,[.,[.,.]]]],.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,[.,[.,[[.,.],.]]]],.],[[.,.],.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[.,[[[[.,.],.],.],.]],[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[.,[[[[.,.],.],.],.]],.],.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]],.]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[[[[.,.],.],.],.]],[.,.]],[.,.]],.]
[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]=>[[[[[.,.],[[[.,.],.],.]],[.,.]],[.,.]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[[[[[.,.],.],.],.],.],[.,.]],.]]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[[[.,[.,.]],[.,.]],.]],.],.]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,[.,.]],[[[.,[.,.]],.],.]]],.]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[.,[.,[[[.,[[.,[.,.]],.]],[[.,.],.]],.]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[.,[.,[[[.,[.,.]],[.,.]],[[[.,.],.],.]]]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,[.,[[.,.],.]]],.]],.]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],.]]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],.],[[.,[.,.]],.]]],.]]
[1,1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,.],[.,[[.,.],.]]]],.]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[.,[[[.,[.,.]],.],.]],[.,.]],.]]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[.,[.,.]],[[.,.],.]],[[.,.],.]]]]
[1,1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[.,[.,.]],[[.,[[[.,.],.],[.,.]]],.]]]
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[.,[.,[[[.,[.,.]],.],[[[.,.],[.,.]],.]]]]
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[[.,[.,[.,.]]],.]],.]],.]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[.,[.,[.,.]]],[.,.]],.],.]]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[[[.,.],[.,[.,.]]],[.,[[.,.],.]]],.]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,.],[[[[.,[.,[.,.]]],.],[.,.]],.]]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[[.,.],[.,[.,.]]],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[[.,[.,[.,.]]],.]],.]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[[.,[[.,.],.]],[.,[.,.]]],[[.,.],.]]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[[.,.],[.,[.,[.,.]]]],.]],.]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[.,[[[.,.],[[.,.],[.,[.,.]]]],[[.,.],.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[.,[[[.,[[.,[[.,.],.]],.]],[.,[.,.]]],.]]
[1,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[[[.,.],[.,.]],.],[.,[.,.]]]],.]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[.,[[[[.,.],[.,[[.,.],.]]],[.,[.,.]]],.]]
[1,1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[[[.,.],.],[.,.]],[.,[.,.]]]],.]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[[.,.],[.,[.,.]]]]],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,.]]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[.,[[[.,.],[.,.]],.]],.],[.,.]]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],[[[.,[.,.]],.],.]]],[.,.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[.,[[.,.],.]],[[.,.],.]],[.,.]]]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[[[.,.],[.,.]],[[[.,.],.],[.,.]]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,[.,[[.,.],.]]],.]],[.,.]]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[[.,[[.,.],[.,.]]],.],[.,.]]]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[[.,.],.],[[.,[.,.]],.]]],[.,.]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,.],[.,[[.,.],.]]]],[.,.]]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[.,[[[.,.],.],.]],[.,.]],[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[[[.,.],[[.,.],.]],[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[.,[[.,.],[[.,[[[.,.],.],[.,.]]],[.,.]]]]
[1,1,1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[.,[.,[[[.,.],.],[[[.,.],[.,.]],[.,.]]]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[[[.,[.,.]],.],.],.],.],[[[.,.],.],.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[[.,[[.,.],.]],.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[.,[.,.]],[.,[.,[[[[[.,.],.],.],.],.]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[[[[.,.],.],.],[.,.]]]]]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,[[.,[[.,.],.]],.]]],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[[[.,.],.],[[.,.],.]],.],.]]
[1,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,[.,.]],[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[[.,[.,.]],[.,[.,.]]],.]],.],.]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,[[.,[.,.]],[.,.]]],.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[.,[[[.,[.,.]],.],[[[.,.],[.,[.,.]]],.]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[[.,[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]],.]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[[[.,[.,.]],.],[[.,.],.]],.],.]],.]
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[[.,[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]],.]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]],.]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[[[.,.],.],[.,.]],[[[.,[[.,.],.]],.],.]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[[[.,.],.],[.,.]],[[[.,.],.],[[.,.],.]]]
[1,0,1,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[[[.,.],.],[.,[[[.,[.,.]],[.,[.,.]]],.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[[[[.,.],.],[[[.,[[.,[.,.]],.]],.],.]],.]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[[[[.,.],.],[[[.,[.,.]],.],[[.,.],.]]],.]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[.,.],[.,[.,[.,.]]]],.]]],.]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[[.,[.,[[.,.],.]]],[.,[[.,[.,.]],.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[[.,.],[[[.,[[.,.],.]],.],[.,.]]],.],.]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],[[[.,.],.],[[.,.],[.,.]]]],.],.]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]],.],.]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[[.,[[.,.],.]],.],.]],[.,.]],.],.]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[[.,.],.],[[.,.],.]]],[.,.]],.],.]
[1,0,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[[.,.],[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0]=>[[.,.],[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[[[.,.],.],[[.,.],.]],.],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[.,.],[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[[.,.],[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[[.,.],[.,[.,.]]],.]],.],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[.,[[[.,[[.,.],.]],.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[.,[[[.,.],.],[[[.,.],[.,[.,.]]],[.,.]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,[[.,[[.,.],.]],.]]],.]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[[[.,.],.],[[.,.],.]],.],.]],[.,.]]
[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]=>[[[.,[.,[.,.]]],.],[[[.,.],[.,[.,.]]],.]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[[.,[.,[[.,.],.]]],.],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[[[[.,.],[.,.]],.],[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[.,[[[.,[.,.]],.],.]],[[.,[.,[.,.]]],.]]
[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]=>[[[[.,[.,[.,[[.,[.,.]],.]]]],.],[.,.]],.]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],[.,[[.,[.,.]],.]]]],[.,.]],.]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[.,[.,[[.,[.,.]],.]]]],.],[[.,.],.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],[.,[[.,[.,.]],.]]],.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[.,[[.,[.,.]],.]]],.]],[[.,.],.]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[[.,[.,.]],.],[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[.,[[.,.],.]],[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[.,[.,.]],.],[.,[[.,[[.,.],.]],[.,.]]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[.,[[.,.],.]],[.,[[.,[[.,.],.]],[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]],.]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]],.]
[1,1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]],.]
[1,1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]],.]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[[[.,[.,.]],.],[.,[.,.]]],.],[.,.]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[.,[[[[.,[[.,[.,.]],.]],[.,[.,.]]],.],.]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[.,[[[[.,[.,.]],.],[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[.,[[[.,[[.,.],.]],[[.,.],[.,.]]],[.,.]]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[[[.,[.,[[.,.],.]]],.],[.,[.,.]]],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[.,[[[.,[[.,.],[[.,.],.]]],[.,[.,.]]],.]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[[.,[.,[.,.]]],.],[[[.,.],[.,.]],.]]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,[.,[[.,.],.]]],.],[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[[[.,.],[.,.]],.],[.,.]]],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,[[[.,[.,.]],.],.]],[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[[.,.],[[.,.],.]],[.,.]]],[.,.]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[.,[[.,[[.,[.,.]],.]],[[[.,[.,.]],.],.]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,[[.,.],.]],[.,.]]],[[.,.],.]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.],.]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[.,[.,[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]]]
[1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,[[.,[.,.]],.]],.]]]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[[[[[.,.],.],.],.],[.,.]]]],.],.]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[[[[.,.],.],.],[.,.]]]],.],.],.]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[[[.,.],.],[.,.]]]],.],.],.],.]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,[[.,.],[.,.]]]],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[[[[.,.],.],.],.],.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[[[[.,.],.],.],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[[[.,.],.],.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[.,.],.],[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[[[[.,[.,.]],.],.],.]],.]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]],.],.]
[1,1,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[[[.,[.,.]],[[.,[.,[.,.]]],[.,[.,.]]]],.]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]],[.,.]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]],[.,.]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[[.,[[.,.],.]],.],.],.],[[.,.],.]],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[[[.,.],[.,.]],.],.],.],[[.,.],.]],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]],.]
[1,0,1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[.,.],.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[.,.],.],[[.,.],[.,[[[.,.],[.,.]],.]]]]
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[.,.],.],[.,[[[.,.],[[.,.],[.,.]]],.]]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[[[.,.],.],[[.,.],.]],[.,[[.,[.,.]],.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[[.,.],[[.,.],.]],[.,[[[.,.],[.,.]],.]]]
[1,0,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[.,.],.],[[[.,.],[[.,.],[.,[.,.]]]],.]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[[.,.],.],.],[[[.,[.,.]],[.,[.,.]]],.]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[[.,.],[[.,.],.]],[[[.,.],[.,[.,.]]],.]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[[[.,.],.],.],[[[.,[.,[.,.]]],[.,.]],.]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[[[.,.],.],[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[[.,[[.,.],.]],.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[[.,[[.,.],.]],.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[[.,[[.,.],.]],.],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,[[.,.],[[.,.],.]]],.],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,[[.,[[.,.],.]],.]],.],[[.,[.,.]],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.]
[1,0,1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[[[[.,.],.],[.,[[[.,.],[.,.]],[.,.]]]],.]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,.],[[.,[[.,.],.]],[[.,.],[.,.]]]],.]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[[.,.],[[.,.],[[.,.],.]]],[.,[.,.]]],.]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[[[[.,.],[[.,.],.]],[.,.]],[.,[.,.]]],.]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,[[.,.],.]],[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[[.,[[.,.],.]],[[.,.],.]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,[[.,.],[[.,.],.]]],[[.,.],[.,.]]],.]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,[[.,[[.,.],.]],.]],[[.,.],[.,.]]],.]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,[[.,.],[[.,.],.]]]],[.,.]],.]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[[[.,.],.],[.,[[.,[.,.]],.]]],[.,.]],.]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[[.,[[.,.],.]],[.,[[.,.],.]]],[.,.]],.]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[[[[[.,.],.],[[.,[.,[.,.]]],.]],[.,.]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[[[[[[.,.],.],.],.],.],[.,[[.,.],.]]],.]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[[[[[.,.],.],.],.],[.,[[[.,.],.],.]]],.]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[[[.,.],.],.],[.,[[[[.,.],.],.],.]]],.]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[[.,.],[[.,.],.]]],[.,.]],[[.,.],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],[[.,.],.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]]
[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]=>[.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[[[[.,.],.],.],.],.],.]]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[[.,[[.,.],.]],.]],.]],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[[[[.,.],.],.],.],.]],[.,.]],[.,.]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[[[.,.],.],.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[[[[[.,.],.],.],.],.]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[[[[.,.],.],.],.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[[.,.],[[[.,.],.],.]],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[[[.,.],[[.,.],.]],.],.],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[[[[.,.],[.,.]],.],.],.],[[.,.],[.,.]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[.,[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[[[[[.,.],.],.],.],.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[[.,[.,.]],[.,[[[[[.,.],.],.],.],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,[[.,.],.]],.]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,.],[.,.]],[[.,[[.,.],[[.,.],.]]],.]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[.,[[.,[[.,.],.]],.]],.]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,.],[.,[[.,.],.]]],[.,.]],[[.,.],.]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,.],[.,[[.,.],.]]],[[.,[[.,.],.]],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[[.,.],[[.,.],.]]]],[[.,.],.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[[.,[[.,.],.]],.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,[[.,.],.]],[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],[[.,.],.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[[.,[[.,.],.]],.]]],.]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,.],[[.,[[.,.],.]],[[.,.],.]]],.]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[[.,.],[[.,.],.]]],.]],.]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[[.,.],[[.,.],.]]],.]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[[.,[[.,.],.]],.]],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[[.,.],[[.,.],.]]],[[.,.],.]],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[[.,[[.,.],.]],.]],[[.,.],.]],.]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],[[.,.],[[.,.],.]]]],.],.]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],[[.,[[.,.],.]],.]]],.],.]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[[.,.],.]],[[.,.],.]]],.],.]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[[.,.],[[.,.],.]]],.]],.],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[[.,[[.,.],.]],.]],.]],.],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
[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]=>[[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]],.]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]],.]
[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]=>[[.,.],[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[[[[[.,.],.],.],.],.],.],.],[[[.,.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[[[[[.,.],.],.],.],.],.],[[[[.,.],.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[[[[[.,.],.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[[.,.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[.,.],.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[.,[[[.,.],.],.]],.],.],.],.],.],.]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,[[[[.,.],.],.],.]],.],.],.],.],.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[[[[[.,.],.],.],.],.]],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[[[[[[.,.],.],.],.],.],.]],.],.],.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]]
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]]
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[[.,.],[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]],.]
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]]]
[1,1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,.],.]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[[[[[.,.],.],.],.],.]],.]]]]]
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]],.]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.],.]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[[[[[[.,.],.],.],.],.],.],.]],.],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[[[[.,.],.],.],[[[[[.,.],.],.],.],.]],.],.]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[[[.,.],.],.],[[[[[.,[.,.]],.],.],.],.]],.]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]],.]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[[[[.,[.,.]],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]]]
[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.],.]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[.,[[[[[[.,.],.],.],[.,[.,[.,.]]]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],[.,.]],[.,[.,[.,.]]]],.],.],.]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]]]
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[[[[[.,.],.],.],.],[[.,.],[.,.]]],[.,.]],.]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[[[[.,.],.],.],.],[[.,[.,.]],.]],[.,.]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[[[[.,[.,.]],.],.],.],.],.],[[.,.],.]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[[[[[[.,.],.],.],.],.],.],.]],[.,.]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[[[[[.,.],.],.],.],.],.]],[[.,.],.]],.]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,[[[[[.,.],.],.],.],.]],[[[.,.],.],.]],.]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,[[[[.,.],.],.],.]],[[[[.,.],.],.],.]],.]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,[[[.,.],.],.]],[[[[[.,.],.],.],.],.]],.]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[[[[[.,.],.],.],.],.],.]],.]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[[[[[.,.],.],.],.],.],.],.]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[[[.,.],[.,.]],[.,.]]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]],.]
[1,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[[[[.,[.,.]],.],.],.],.],[.,.]]]]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]],.]
[1,1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]
[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[[.,.],[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[[.,.],[.,[[[[[[[.,.],.],.],.],.],.],.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0,0]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]]
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[.,[.,[[[[[[.,.],.],.],.],.],[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[[[[[.,.],.],.],.],[.,[[[.,.],.],.]]]]]
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[[[[.,.],.],.],[.,[[[[.,.],.],.],.]]]]]
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[[[.,.],.],[.,[[[[[.,.],.],.],.],.]]]]]
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[[.,.],[.,[[[[[[.,.],.],.],.],.],.]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]],.]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],[[[[.,.],.],.],.]],.],.],.],.]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[.,.],.],[[[.,.],.],.]],.],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[.,.],.],.],[[.,.],.]],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[[[[[.,.],.],.],.],[.,[[.,.],.]]]]]]
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[[[[.,.],.],.],[.,[[[.,.],.],.]]]]]]
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[[[.,.],.],[.,[[[[.,.],.],.],.]]]]]]
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[[[[[.,.],.],.],.],.]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[[[[.,.],.],.],.],[.,.]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[1,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[.,[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[.,[[[[[[[.,.],.],.],.],.],[[[.,.],.],.]],.]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[[.,.],[[[.,.],.],.]],.],.],.],.]]]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[[[.,.],.],[[.,.],.]],.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[[[[.,[.,.]],.],.],.],.],.],[[.,.],.]]]
[1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]]
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]]
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.]]
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]]
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]]
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,[[.,.],.]],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],[[.,.],.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],[[.,.],.]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],[[.,.],.]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],[[.,.],.]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],[[.,.],.]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],[[.,.],.]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],[[.,.],.]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],[[.,.],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],[[.,.],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],[[.,.],.]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],[[.,.],.]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],[[.,.],.]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],[[.,.],.]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[[.,.],.]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]]
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]]
[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]=>[.,[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.]]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],.]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],.]]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]
[1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],.]]
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],.]]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],.]]
[1,1,0,0,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]]
[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,[.,.]],.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,[.,.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],.]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],.]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[[[.,[.,.]],[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[[[.,.],[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[[.,.],[.,.]],.],[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[[.,.],[[[.,.],[.,[[.,.],[[.,.],[[.,.],.]]]]],.]]
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,[[.,.],[[.,.],[[.,.],.]]]]],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,.],[[[[.,.],[.,.]],.],[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[[[.,.],[[[.,[.,.]],.],[.,[[.,.],[[.,.],.]]]]],.]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[[.,.],[.,[[.,.],[[.,.],.]]]]],.],[.,.]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],[.,[.,[[.,.],[[.,.],.]]]]],.],[.,.]],.]
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,.],[.,[[.,.],[[.,.],.]]]],.]]]
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[.,.],[.,[[.,.],[[.,.],.]]]],.]]],.]
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[[.,.],[.,.]],.],[[.,[.,[[.,.],[[.,.],.]]]],.]]
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,[.,[[.,.],[[.,.],.]]]],.]],.]]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,[.,[[.,.],[[.,.],.]]]],.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[[.,.],[[.,.],[[[[.,.],[.,.]],.],[.,[[.,.],.]]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[[[[.,.],[.,.]],.],[.,[[.,.],.]]]]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[[[[.,.],[.,.]],.],[[[.,[.,.]],.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[[.,.],[[[.,.],[[[.,[.,.]],.],[.,[[.,.],.]]]],.]]
[1,0,1,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[[.,[.,.]],.],[.,[[.,.],.]]]],.]],.]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[[[.,.],[[.,.],[.,.]]],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[[[[.,.],[.,[.,.]]],.],[[.,.],[.,[[.,.],.]]]],.]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[[[.,.],[[[.,.],[.,.]],.]],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[[[[.,.],[[.,[.,.]],.]],.],[.,[.,[[.,.],.]]]],.]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[[.,.],[[.,.],[.,[[.,.],.]]]],.],[.,.]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],[[[.,[[.,.],[.,[[.,.],.]]]],.],[.,.]]],.]
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[[[[[[.,.],[.,.]],.],[.,[.,[[.,.],.]]]],.],[.,.]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0,0]=>[[.,.],[[[[[.,.],[.,[.,[[.,.],.]]]],.],[.,.]],.]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[[[.,[.,[.,[[.,.],.]]]],.],[.,.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[[.,.],[.,[[.,.],.]]],.]]]]
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>[[[.,.],[.,[[.,.],[[[.,.],[.,[[.,.],.]]],.]]]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[[[[.,.],[.,.]],.],[.,[[[.,.],[.,[[.,.],.]]],.]]]
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[[.,.],[[[.,.],[.,[[[.,.],[.,[[.,.],.]]],.]]],.]]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,[[[.,.],[.,[[.,.],.]]],.]]],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[.,.],[[[[.,.],[.,.]],.],[[.,[.,[[.,.],.]]],.]]]
[1,0,1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[[[.,.],[[[.,[.,.]],.],[[.,[.,[[.,.],.]]],.]]],.]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[[.,.],[[.,[.,[[.,.],.]]],.]]],.],[.,.]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],[.,[[.,[.,[[.,.],.]]],.]]],.],[.,.]],.]
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,.],[[.,[.,[[.,.],.]]],.]],.]]]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[.,.],[[.,[.,[[.,.],.]]],.]],.]]],.]
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[[[.,.],[.,.]],.],[[.,[[.,[.,[[.,.],.]]],.]],.]]
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,[[.,[.,[[.,.],.]]],.]],.]],.]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,[[.,[.,[[.,.],.]]],.]],.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[[[.,.],[.,.]],.],[.,.]]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[[.,.],[[[[.,.],[.,.]],.],[.,.]]]]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[[[[.,.],[.,.]],.],[.,[[[[.,.],[.,.]],.],[.,.]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0]=>[[.,.],[[[.,.],[.,[[[[.,.],[.,.]],.],[.,.]]]],.]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,[[[[.,.],[.,.]],.],[.,.]]]],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[.,.],[[[[.,.],[.,.]],.],[[[.,[.,.]],.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[[[.,.],[[[.,[.,.]],.],[[[.,[.,.]],.],[.,.]]]],.]
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[[.,.],[[[.,[.,.]],.],[.,.]]]],.],[.,.]]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],[.,[[[.,[.,.]],.],[.,.]]]],.],[.,.]],.]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,.],[[[.,[.,.]],.],[.,.]]],.]]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[.,.],[[[.,[.,.]],.],[.,.]]],.]]],.]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[[[[.,.],[.,.]],.],[[.,[[[.,[.,.]],.],[.,.]]],.]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,[[[.,[.,.]],.],[.,.]]],.]],.]]
[1,0,1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,[[[.,[.,.]],.],[.,.]]],.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[[[.,.],[[.,.],[.,.]]],.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,.],[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[[[[.,.],[.,.]],.],[.,[.,.]]],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[[[[.,.],[.,[.,.]]],.],[[.,.],[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[[[.,[.,[.,.]]],.],[[.,.],[.,.]]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[[.,.],[[[[.,.],[[[.,.],[.,.]],.]],.],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[[[.,.],[[[.,[[[.,.],[.,.]],.]],.],[.,[.,.]]]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[[[[.,.],[.,.]],.],[[.,[.,.]],.]],.],[.,[.,.]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[[.,.],[[[[[.,.],[[.,[.,.]],.]],.],[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[[[.,[[.,[.,.]],.]],.],[.,[.,.]]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[[.,.],[[.,.],[[.,.],[.,.]]]],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[[.,.],[[[.,.],[[.,.],[.,.]]],.]],.],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[[[[.,.],[.,[[.,.],[.,.]]]],.],[[.,.],[.,.]]],.]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[.,.],[[.,[[.,.],[.,.]]],.]],.],[.,[.,.]]],.]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[[[[[.,.],[[.,.],[.,.]]],.],[.,.]],.],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[[[.,.],[.,[.,.]]],.],[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],[[[.,.],[.,.]],.]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[[.,.],[[[.,.],[.,[.,.]]],.]],.],[[.,[.,.]],.]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[[[[.,.],[.,[.,[.,.]]]],.],[[[.,.],[.,.]],.]],.]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[[[[.,.],[[.,[.,[.,.]]],.]],.],[[.,[.,.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[[.,.],[[.,.],[[[[.,.],[[.,.],[.,.]]],.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0,1,0]=>[[[.,.],[.,[[[[.,.],[[.,.],[.,.]]],.],[.,.]]]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[[[[.,.],[.,.]],.],[[[.,[[.,.],[.,.]]],.],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[[.,.],[[[.,[[.,.],[.,.]]],.],[.,.]]],.]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[[[[.,.],[.,.]],.],[.,[.,.]]],.],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],[[[[[.,[.,.]],.],[.,[.,.]]],.],[.,.]]],.]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[[[[.,.],[.,[.,.]]],.],[.,.]]],.],[.,.]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],[[[.,[.,[.,.]]],.],[.,.]]],.],[.,.]],.]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[[[[.,.],[.,[.,.]]],.],[.,.]],.]]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[[[.,.],[.,[.,.]]],.],[.,.]],.]]],.]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[[[[.,.],[.,.]],.],[[[[.,[.,[.,.]]],.],[.,.]],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[[[.,[.,[.,.]]],.],[.,.]],.]],.]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[[[.,[.,[.,.]]],.],[.,.]],.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[[.,.],[.,.]],.],[.,[[.,.],[[[.,.],[.,.]],.]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0]=>[[.,.],[[[.,.],[.,[[.,.],[[[.,.],[.,.]],.]]]],.]]
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,[[.,.],[[[.,.],[.,.]],.]]]],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[.,.],[[[[.,.],[.,.]],.],[.,[[[.,.],[.,.]],.]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[[[.,.],[[[.,[.,.]],.],[.,[[[.,.],[.,.]],.]]]],.]
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[[.,.],[.,[[[.,.],[.,.]],.]]]],.],[.,.]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],[.,[.,[[[.,.],[.,.]],.]]]],.],[.,.]],.]
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,.],[.,[[[.,.],[.,.]],.]]],.]]]
[1,0,1,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[.,.],[.,[[[.,.],[.,.]],.]]],.]]],.]
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[[[[.,.],[.,.]],.],[[.,[.,[[[.,.],[.,.]],.]]],.]]
[1,0,1,1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,[.,[[[.,.],[.,.]],.]]],.]],.]]
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,[.,[[[.,.],[.,.]],.]]],.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[[.,.],[[.,.],[[[[.,.],[.,.]],.],[[.,[.,.]],.]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[.,.],[.,[[[[.,.],[.,.]],.],[[.,[.,.]],.]]]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[[.,.],[.,.]],.],[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[[.,.],[[[.,.],[[[.,[.,.]],.],[[.,[.,.]],.]]],.]]
[1,0,1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[[.,[.,.]],.],[[.,[.,.]],.]]],.]],.]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[[[.,.],[[.,.],[.,.]]],.],[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[[[[.,.],[.,[.,.]]],.],[[.,.],[[.,[.,.]],.]]],.]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[[[.,.],[[[.,.],[.,.]],.]],.],[.,[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[[[[.,.],[[.,[.,.]],.]],.],[.,[[.,[.,.]],.]]],.]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[[.,.],[[.,.],[[.,[.,.]],.]]],.],[.,.]]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],[[[.,[[.,.],[[.,[.,.]],.]]],.],[.,.]]],.]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[[[[[[.,.],[.,.]],.],[.,[[.,[.,.]],.]]],.],[.,.]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[[.,.],[[[[[.,.],[.,[[.,[.,.]],.]]],.],[.,.]],.]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[[[.,[.,[[.,[.,.]],.]]],.],[.,.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[[.,.],[[.,[.,.]],.]],.]]]]
[1,0,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0]=>[[[.,.],[.,[[.,.],[[[.,.],[[.,[.,.]],.]],.]]]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[[[[.,.],[.,.]],.],[.,[[[.,.],[[.,[.,.]],.]],.]]]
[1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[[.,.],[[[.,.],[.,[[[.,.],[[.,[.,.]],.]],.]]],.]]
[1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,[[[.,.],[[.,[.,.]],.]],.]]],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[.,.],[[[[.,.],[.,.]],.],[[.,[[.,[.,.]],.]],.]]]
[1,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[[[.,.],[[[.,[.,.]],.],[[.,[[.,[.,.]],.]],.]]],.]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[[.,.],[[.,[[.,[.,.]],.]],.]]],.],[.,.]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],[.,[[.,[[.,[.,.]],.]],.]]],.],[.,.]],.]
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,.],[[.,[[.,[.,.]],.]],.]],.]]]
[1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[.,.],[[.,[[.,[.,.]],.]],.]],.]]],.]
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[.,.],[.,.]],.],[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[.,[[.,[[.,.],.]],[[.,[[.,[.,.]],[[.,.],.]]],.]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[.,[[[.,.],[[[.,.],.],[.,.]]],[[[.,.],.],[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[[[[.,.],.],[.,.]],[.,[[[[[.,.],.],[.,.]],.],.]]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[.,[[[[[.,.],.],[.,.]],.],.]]],[.,.]],.],.]
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[.,[[[.,[[[.,[.,.]],.],.]],[[[.,[.,.]],.],.]],.]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],[[.,.],.]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],.],[[.,.],.]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,[[.,.],[[.,.],[.,.]]]],[[.,.],.]]],.]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,[[.,.],[[.,.],[.,.]]]],.]],[[.,.],.]]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,[[.,.],[[.,.],[.,.]]]],.]],.]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,[[.,.],.]],[[.,.],[.,.]]],[[.,[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,[[.,.],.]],[[.,.],[.,.]]],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,[[.,.],[.,.]]],[[.,.],.]]]],.]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,.],.],[[.,[[.,[[.,.],[.,.]]],[[.,.],.]]],.]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,.],[[.,[[.,.],[.,.]]],.]]],[[.,.],.]]
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,.],[[.,[[.,.],[.,.]]],.]]],.]],.]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[[[.,.],.],[[.,[[.,[[.,.],[.,.]]],.]],[[.,.],.]]]
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,[[.,[[.,.],[.,.]]],.]],.]]],.]]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,.],[[.,[[.,.],.]],[.,.]]],[[.,[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,.],[[.,[[.,.],.]],[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,[[.,[[.,.],.]],[.,.]]],[[.,.],.]]],.]]
[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]=>[[[.,[[.,[[.,[[.,[[.,.],.]],[.,.]]],.]],.]],.],.]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[.,[[.,.],.]],.],[[.,[.,.]],[[.,[[.,.],.]],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,[[.,.],.]],.],[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[.,.],[[.,.],.]],[[.,[.,.]],[[.,[[.,.],.]],.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,.],[[.,.],.]],[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,.],[[.,[.,.]],[[.,.],.]]]]],.]
[1,0,1,0,1,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[.,.],.],[[.,[[.,.],[[.,[.,.]],[[.,.],.]]]],.]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[[.,[[.,.],.]],[[.,[.,.]],[[.,.],.]]]],.]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[[[.,.],.],[[.,.],[[.,[[.,[.,.]],[[.,.],.]]],.]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]],[[.,.],.]]
[1,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,.],[[.,.],[[.,[.,.]],.]]]],.]],.]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[[[.,.],.],[[.,[[.,.],[[.,[.,.]],.]]],[[.,.],.]]]
[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,[[.,.],[[.,[.,.]],.]]],.]]],.]]
[1,1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,[[.,.],[[.,[.,.]],.]]],.]],.]]]
[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]=>[[[.,[[.,[[.,[[.,.],.]],[[.,[.,.]],.]]],.]],.],.]
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[.,.],.],[[.,.],[[.,[[.,[.,.]],.]],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[.,[[.,[[.,.],.]],[[.,[[.,[.,.]],.]],[[.,.],.]]]]
[1,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,.],[[.,[[.,[.,.]],.]],.]]]],.]]
[1,1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,.],[[.,[[.,[.,.]],.]],.]]],.]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,0]=>[[[.,[[.,[[.,.],.]],[[.,[[.,[.,.]],.]],.]]],.],.]
[1,1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,.],[[.,.],[.,[[.,.],.]]]],[[.,[[.,.],.]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,.],[[.,.],[.,[[.,.],.]]]],[[.,.],[[.,.],.]]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,[[.,.],[.,[[.,.],.]]]],[[.,.],.]]],.]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,[[.,.],[.,[[.,.],.]]]],.]],[[.,.],.]]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[[.,[[.,.],[.,[[.,.],.]]]],.]],.]],.],.]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[.,.],.],[[.,[.,[[.,.],.]]],[[.,[[.,.],.]],.]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,.],.],[[.,[.,[[.,.],.]]],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,[.,[[.,.],.]]],[[.,.],.]]]],.]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,[.,[[.,.],.]]],[[.,.],.]]],.]]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,.],[[.,[.,[[.,.],.]]],.]]],[[.,.],.]]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[[.,.],[[.,[.,[[.,.],.]]],.]]],.]],.],.]
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[.,[[.,.],[[.,[[.,[.,[[.,.],.]]],.]],[[.,.],.]]]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0,1,0]=>[[[.,[[.,.],[[.,[[.,[.,[[.,.],.]]],.]],.]]],.],.]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[.,[.,[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[.,[.,[[.,[[.,.],.]],.]]],[[.,.],[[.,.],.]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,[[.,[.,[[.,[[.,.],.]],.]]],[[.,.],.]]],.],.]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[.,[.,[[.,[[.,.],.]],.]]],.]],[[.,.],.]],.]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[.,[[.,[.,[[.,[[.,.],.]],.]]],.]],.],[[.,.],.]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[.,[.,[[.,.],[[.,.],.]]]],[[.,[[.,.],.]],.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[.,[.,[[.,.],[[.,.],.]]]],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,[[.,[.,[[.,.],[[.,.],.]]]],[[.,.],.]]],.],.]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[.,[.,[[.,.],[[.,.],.]]]],.]],[[.,.],.]],.]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[.,[[.,[.,[[.,.],[[.,.],.]]]],.]],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[.,[[.,.],.]],.],[[.,.],[.,[[.,[[.,.],.]],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[.,[[.,.],.]],.],[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[.,.],[[.,.],.]],[[.,.],[.,[[.,[[.,.],.]],.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[.,.],[[.,.],.]],[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[.,.],.],[[.,[[.,.],.]],[.,[[.,[[.,.],.]],.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[.,.],.],[[.,[[.,.],.]],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[.,[[.,[[.,[[.,.],.]],.]],[.,[[.,[[.,.],.]],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[.,[[.,[[.,.],.]],.]],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[.,[[.,[[.,.],[[.,.],.]]],[.,[[.,[[.,.],.]],.]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[.,[[.,.],[[.,.],.]]],[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,.],[[.,.],[.,[[.,.],.]]]]]],.]
[1,0,1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[[[.,.],.],[[.,[[.,.],[[.,.],[.,[[.,.],.]]]]],.]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[.,[[.,[[.,[[.,.],.]],[[.,.],[.,[[.,.],.]]]]],.]]
[1,0,1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[[[.,.],.],[[.,.],[[.,[[.,.],[.,[[.,.],.]]]],.]]]
[1,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[.,[[.,[[.,.],.]],[[.,[[.,.],[.,[[.,.],.]]]],.]]]
[1,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,[[.,.],.]],[.,[[.,.],.]]]]],.]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,[[.,.],.]],[.,[[.,.],.]]]],.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,[[.,[[.,.],.]],.]],[.,[[.,.],.]]]],.],.]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,[[.,.],[[.,.],.]]],[.,[[.,.],.]]]],.],.]
[1,0,1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[[[.,.],.],[[.,.],[[.,.],[[.,[.,[[.,.],.]]],.]]]]
[1,1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[.,[[.,[[.,.],.]],[[.,.],[[.,[.,[[.,.],.]]],.]]]]
[1,1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[.,[[.,.],[[.,[[.,.],.]],[[.,[.,[[.,.],.]]],.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[.,[[.,[[.,.],.]],.]],[[.,[.,[[.,.],.]]],.]],.]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[.,[[.,.],[[.,.],.]]],[[.,[.,[[.,.],.]]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],[[.,.],.]]
[1,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],.]],.]]
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[[[.,.],.],[[.,[[.,.],[[.,.],[.,.]]]],[[.,.],.]]]
[1,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,[[.,.],[[.,.],[.,.]]]],.]]],.]]
[1,1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,[[.,.],[[.,.],[.,.]]]],.]],.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,[[.,.],.]],[[.,.],[.,.]]]],[[.,.],.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[[.,[[.,.],.]],[[.,.],[.,.]]]],.]],.],.]
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[[[.,.],.],[[.,.],[[.,[[.,.],[.,.]]],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[.,[[.,[[.,.],.]],[[.,[[.,.],[.,.]]],[[.,.],.]]]]
[1,1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,.],[[.,[[.,.],[.,.]]],.]]]],.]]
[1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,.],[[.,[[.,.],[.,.]]],.]]],.]]]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[[[.,[[.,[[.,.],.]],[[.,[[.,.],[.,.]]],.]]],.],.]
[1,1,0,1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,[[.,[[.,.],[.,.]]],.]],.]]]]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[.,[[.,[[.,.],[.,.]]],.]],.]],.]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,.],[[.,[[.,.],.]],[.,.]]]],[[.,.],.]]]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[[.,.],[[.,[[.,.],.]],[.,.]]]],.]],.],.]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[.,[[.,.],[[.,[[.,[[.,.],.]],[.,.]]],[[.,.],.]]]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[[[.,[[.,.],[[.,[[.,[[.,.],.]],[.,.]]],.]]],.],.]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,[[.,[[.,.],.]],[.,.]]],.]],.]],.]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[.,[[.,[[.,.],.]],.]],[.,.]]],[[.,.],.]],.]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[[.,[[.,[[.,.],.]],.]],[.,.]]],.],[[.,.],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[.,[[.,.],[[.,.],.]]],[.,.]]],[[.,.],.]],.]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[[.,[[.,.],[[.,.],.]]],[.,.]]],.],[[.,.],.]]
[1,0,1,0,1,1,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[[[.,.],.],[[.,.],[[.,.],[[.,[.,.]],[[.,.],.]]]]]
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[.,[[.,[[.,.],.]],[[.,.],[[.,[.,.]],[[.,.],.]]]]]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[.,[[.,.],[[.,[[.,.],.]],[[.,[.,.]],[[.,.],.]]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[.,[[.,[[.,.],.]],.]],[[.,[.,.]],[[.,.],.]]],.]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[.,[[.,.],[[.,.],.]]],[[.,[.,.]],[[.,.],.]]],.]
[1,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]],.]]
[1,1,0,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,.],[[.,.],[[.,[.,.]],.]]]],.]]]
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,[[.,.],.]],[[.,.],[[.,[.,.]],.]]]],.],.]
[1,1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,[[.,.],[[.,[.,.]],.]]],.]]]]
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[.,[[.,.],[[.,[.,.]],.]]],.]],.]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,.],[[.,[[.,.],.]],[[.,[.,.]],.]]]],.],.]
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,[[.,.],.]],[[.,[.,.]],.]]],.]],.]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[.,[[.,[[.,.],.]],.]],[[.,[.,.]],.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[.,[[.,.],[[.,.],.]]],[[.,[.,.]],.]],[[.,.],.]]
[1,1,0,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],[[.,[[.,[.,.]],.]],.]]]]]
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[[[.,[[.,.],.]],[[.,.],[[.,[[.,[.,.]],.]],.]]],.]
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[[[.,.],[[.,[[.,.],.]],[[.,[[.,[.,.]],.]],.]]],.]
[1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,[[.,.],.]],.],[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,0,1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,.],[[.,.],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,1,0,1,1,1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0,0,0]=>[.,[[.,.],[.,[[.,.],[[[[.,[.,.]],[.,.]],.],.]]]]]
[1,1,0,1,1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]],.]]]
[1,1,0,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0,0,0]=>[.,[[.,.],[.,[[.,.],[[[[.,[.,.]],.],[.,.]],.]]]]]
[1,1,0,1,1,1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]]]]
[1,1,0,1,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[.,[[.,.],[[[.,[.,.]],[.,[[.,[[.,.],.]],.]]],.]]]
[1,1,0,1,1,1,0,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0]=>[.,[[.,.],[[.,[.,.]],[[.,[.,[.,.]]],[[.,.],.]]]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[[.,.],[[.,.],.]],[.,[.,.]]]],.]]]
[1,1,0,1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>[.,[[.,.],[[[.,[.,.]],[.,[[.,.],[[.,.],.]]]],.]]]
[1,1,0,1,1,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0,0,0]=>[.,[[.,.],[.,[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]]]]
[1,1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[[.,.],[[[[.,.],[.,.]],.],[.,.]]]]]]
[1,1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[.,[[.,.],[[.,[.,.]],[[.,[.,[.,[.,.]]]],[.,.]]]]]
[1,1,0,1,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[[.,.],[[[[.,.],.],[.,.]],[.,.]]]]]]
[1,1,0,1,1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[.,[[.,.],[[.,[.,.]],[.,[[.,.],[[.,[.,.]],.]]]]]]
[1,1,0,1,1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[.,[[.,.],[[[.,.],[[[.,.],.],[[.,[.,.]],.]]],.]]]
[1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[[[.,.],.],[.,.]],[[.,.],.]]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[.,[[.,.],[[[[.,.],[[.,.],.]],[.,[.,[.,.]]]],.]]]
[1,1,0,1,1,0,1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[[[.,.],.],[[.,.],.]],[.,.]]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[.,[[.,.],[[[.,.],[[.,.],.]],[.,[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[.,.],[[[.,[.,[.,.]]],[[[.,.],.],[.,.]]],.]]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[.,[[.,.],[[[.,[.,[.,.]]],[[.,.],.]],[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[.,.],[[[.,.],[[[[.,[.,.]],.],.],[.,.]]],.]]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[.,[[.,.],[[[.,.],[[[.,[.,.]],.],.]],[.,[.,.]]]]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[[.,[.,[[.,[.,.]],.]]],[[.,.],.]],.]]]
[1,1,0,1,1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[[[.,[.,.]],[[.,.],.]],.],.]],.]]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[[[.,.],[.,[.,[.,.]]]],[[.,.],.]],.]]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[[[.,[[.,.],.]],[.,.]],.],.]],.]]]
[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[[.,.],[[[.,[[.,.],[.,.]]],.],.]],.]]]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0,0,0]=>[.,[[.,.],[[.,[.,[[.,[[.,.],[.,.]]],.]]],[.,.]]]]
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0,0]=>[.,[[.,.],[.,[[.,[[[[.,[.,.]],[.,.]],.],.]],.]]]]
[1,1,0,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[.,[[.,.],[[.,[[.,[.,.]],[.,[.,[.,.]]]]],[.,.]]]]
[1,1,0,1,1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0,0,0]=>[.,[[.,.],[.,[[.,[[[[.,[.,.]],.],[.,.]],.]],.]]]]
[1,1,0,1,1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0]=>[.,[[.,.],[.,[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]]]]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0,0]=>[.,[[.,.],[[[.,.],[.,[[.,[[.,.],.]],.]]],[.,.]]]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,0,0]=>[.,[[.,.],[[.,.],[[[.,[.,[.,.]]],[[.,.],.]],.]]]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[.,[[.,.],[[.,[[.,[[.,.],.]],[.,[.,.]]]],[.,.]]]]
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,0,0]=>[.,[[.,.],[[[.,.],[.,[[.,.],[[.,.],.]]]],[.,.]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,0,0,0]=>[.,[[.,.],[.,[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]]]]
[1,1,0,1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,0]=>[.,[[.,.],[.,[[.,[[[[.,.],[.,.]],.],[.,.]]],.]]]]
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0,0,0]=>[.,[[.,.],[[.,.],[[[.,[.,[.,[.,.]]]],[.,.]],.]]]]
[1,1,0,1,1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0,0,0,0]=>[.,[[.,.],[.,[[.,[[[[.,.],.],[.,.]],[.,.]]],.]]]]
[1,1,1,0,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[.,[[[.,[.,.]],.],[[.,[[.,.],[[.,[.,.]],.]]],.]]]
[1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[.,[[[.,[.,.]],.],[.,[[[.,.],[.,.]],[[.,.],.]]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[.,[[[.,[.,.]],.],[[[.,[.,.]],[.,[.,[.,.]]]],.]]]
[1,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[.,[[[.,[.,.]],.],[.,[[[.,.],[[.,.],.]],[.,.]]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[.,[[[.,[.,.]],.],[[.,[.,.]],[.,[[.,.],[.,.]]]]]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[[.,[.,.]],.],[[[.,.],[[[.,.],.],[.,.]]],.]]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[.,[[[.,[.,.]],.],[[[.,.],[[.,.],.]],[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,0]=>[.,[[[.,[.,.]],.],[[[.,[.,[.,.]]],[[.,.],.]],.]]]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[.,[[[.,[.,.]],.],[[[.,.],[[[.,[.,.]],.],.]],.]]]
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0,0]=>[.,[[[.,[.,.]],.],[[.,[.,[[.,[.,.]],.]]],[.,.]]]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,0]=>[.,[[[.,[.,.]],.],[.,[[[.,[.,.]],[[.,.],.]],.]]]]
[1,1,1,0,0,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[.,[[[.,[.,.]],.],[[[.,.],[.,[.,[.,.]]]],[.,.]]]]
[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0,0]=>[.,[[[.,[.,.]],.],[.,[[[.,[[.,.],.]],[.,.]],.]]]]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[.,[[[.,[.,.]],.],[[.,.],[[.,[[.,.],[.,.]]],.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[[.,[[.,[.,.]],.]],.],[[.,[[.,.],[.,.]]],.]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[.,[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[.,[[[.,[[.,[.,.]],.]],.],[[[.,.],[[.,.],.]],.]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[.,[[[.,[[.,[.,.]],.]],.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[.,[[[.,[[.,[.,.]],.]],.],[[.,.],[[.,[.,.]],.]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],[[.,[[.,.],[.,.]]],.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],[[[.,.],[[.,.],.]],.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],[[.,.],[[.,[.,.]],.]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[[.,[.,.]],.]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,[[.,[.,.]],[.,[.,.]]]],.],[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,[[.,[.,.]],[.,[.,.]]]],.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,[[[.,.],[[.,.],.]],.]],.],[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,[[[.,.],[[.,.],.]],.]],.],[[.,.],[.,.]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,[[.,[.,[.,.]]],[.,.]]],.],[[.,[.,.]],.]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,[[.,[.,[.,.]]],[.,.]]],.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,[[.,.],[[.,[.,.]],.]]],.],[[.,[.,.]],.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,[[.,.],[[.,[.,.]],.]]],.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[.,[[.,.],[[.,[.,.]],.]]],.]],.],[.,.]]]
[1,1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,[[[.,.],[.,.]],[[.,.],.]]]],.],[.,.]]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]],.],[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,[[[.,.],[[.,.],.]],[.,.]]]],.],[.,.]]]
[1,1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]],.],[.,.]]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[[.,.],[[[.,.],.],[.,.]]],.]],.],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[[.,.],[[.,.],.]],[.,[.,.]]]],.],[.,.]]]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[[.,[.,[.,.]]],[[.,.],.]],.]],.],[.,.]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[[.,.],[[[.,[.,.]],.],.]],.]],.],[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]],.],[.,.]]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,[[[.,[.,.]],[[.,.],.]],.]]],.],[.,.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]],.],[.,.]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,[[[.,[[.,.],.]],[.,.]],.]]],.],[.,.]]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[.,.],[[.,[[.,.],[.,.]]],.]]],.],[.,.]]]
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[[.,.],[[[[.,[.,.]],[.,.]],.],.]]]],.]]
[1,1,1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]],.]],.]]
[1,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[[.,.],[[[[.,[.,.]],.],[.,.]],.]]]],.]]
[1,1,1,1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]]],.]]
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],[.,[[.,[[.,.],.]],.]]],.]],.]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[[.,[.,.]],[[.,[.,[.,.]]],[[.,.],.]]]],.]]
[1,1,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[[.,.],[[.,.],.]],[.,[.,.]]]],.]],.]]
[1,1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],[.,[[.,.],[[.,.],.]]]],.]],.]]
[1,1,1,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]]],.]]
[1,1,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[[.,.],[[[[.,.],[.,.]],.],[.,.]]]]],.]]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[.,[.,.]],[[.,[.,[.,[.,.]]]],[.,.]]]],.]]
[1,1,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[[.,.],[[[[.,.],.],[.,.]],[.,.]]]]],.]]
[1,1,1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[.,[[.,[[.,[.,.]],[.,[[.,.],[[.,[.,.]],.]]]]],.]]
[1,1,1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,.],[[[.,.],.],[[.,[.,.]],.]]],.]],.]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[[[.,.],.],[.,.]],[[.,.],.]]]],.]]
[1,1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,.],[[.,.],.]],[.,[.,[.,.]]]],.]],.]]
[1,1,1,0,1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[[[.,.],.],[[.,.],.]],[.,.]]]],.]]
[1,1,1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[[[.,.],[[.,.],.]],[.,[[.,.],[.,.]]]]],.]]
[1,1,1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[.,[.,.]]],[[[.,.],.],[.,.]]],.]],.]]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[[.,[.,[.,.]]],[[.,.],.]],[.,[.,.]]]],.]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,.],[[[[.,[.,.]],.],.],[.,.]]],.]],.]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[[.,.],[[[.,[.,.]],.],.]],[.,[.,.]]]],.]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[.,[[.,[.,.]],.]]],[[.,.],.]],.]],.]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[[[.,[.,.]],[[.,.],.]],.],.]],.]],.]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,.],[.,[.,[.,.]]]],[[.,.],.]],.]],.]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[[[.,[[.,.],.]],[.,.]],.],.]],.]],.]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,.],[[[.,[[.,.],[.,.]]],.],.]],.]],.]]
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[.,[.,[[.,[[.,.],[.,.]]],.]]],[.,.]]],.]]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[.,[[[[.,[.,.]],[.,.]],.],.]],.]]],.]]
[1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[.,[[.,[.,.]],[.,[.,[.,.]]]]],[.,.]]],.]]
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[.,[[[[.,[.,.]],.],[.,.]],.]],.]]],.]]
[1,1,1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]]],.]]
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[[.,.],[.,[[.,[[.,.],.]],.]]],[.,.]]],.]]
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[[.,[.,[.,.]]],[[.,.],.]],.]]],.]]
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[.,[[.,[[.,.],.]],[.,[.,.]]]],[.,.]]],.]]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[[.,.],[.,[[.,.],[[.,.],.]]]],[.,.]]],.]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]]],.]]
[1,1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[.,[[[[.,.],[.,.]],.],[.,.]]],.]]],.]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[[.,[.,[.,[.,.]]]],[.,.]],.]]],.]]
[1,1,1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[.,[[[[.,.],.],[.,.]],[.,.]]],.]]],.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],[[[.,.],.],.]]]]]
[1,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[[.,.],[[.,[[[.,.],.],.]],.]]]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[.,[[[[[.,.],.],[.,.]],.],.]]]]
[1,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[[.,[.,.]],[[.,.],[[.,[[.,.],[[[.,.],.],.]]],.]]]
[1,1,0,0,1,1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0]=>[[.,[.,.]],[[.,.],[[.,[[.,[[[.,.],.],.]],.]],.]]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[[.,[.,.]],[.,[[[[.,.],.],[.,.]],[[[.,.],.],.]]]]
[1,1,0,0,1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[[[.,.],.],[[[.,[.,.]],.],.]],.]]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[[.,.],[[[.,.],.],[.,.]]],.],.]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[[.,[[[.,.],.],.]],[.,.]],.],.]]]
[1,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,.],[[.,.],[[[.,.],.],.]]]],.]]
[1,1,0,0,1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,.],[[.,[[[.,.],.],.]],.]]],.]]
[1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,[[[[[.,.],.],[.,.]],.],.]]],.]]
[1,1,0,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,[[.,.],[[[.,.],.],.]]],.]],.]]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,[[.,[[[.,.],.],.]],.]],.]],.]]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[.,[[[[.,[.,.]],.],[.,.]],[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[.,[[[[.,[.,.]],.],[.,.]],[[.,[[[.,.],.],.]],.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[.,[[[.,[.,.]],.],[[[[[.,[.,.]],.],[.,.]],.],.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[.,[[[[.,[.,.]],.],[[.,[.,.]],[[[.,.],.],.]]],.]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],.],[[.,[[[.,[.,.]],.],.]],.]],.]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[.,[[[.,[.,.]],[[[.,.],.],[.,.]]],[[[.,.],.],.]]]
[1,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[[[[.,.],.],[.,[.,.]]],.],.]],.]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[.,[[[.,[[[.,[.,.]],.],.]],[.,.]],[[[.,.],.],.]]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[.,[[[[.,[.,.]],[[.,.],[[[.,.],.],[.,.]]]],.],.]]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[.,[[[[.,[.,.]],[[.,[[[.,.],.],.]],[.,.]]],.],.]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[[[[.,[.,.]],.],[.,.]],.],[.,.]]],.],.]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[.,[[.,[.,.]],[[[.,.],.],.]]],[.,.]],.],.]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[.,[[.,[[[.,[.,.]],.],.]],.]],[.,.]],.],.]]
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,.],[[.,.],[[[.,.],.],.]]]]],.]
[1,1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,.],[[.,[[[.,.],.],.]],.]]]],.]
[1,1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[[.,[[.,[.,.]],[.,[[[[[.,.],.],[.,.]],.],.]]]],.]
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,[[.,.],[[[.,.],.],.]]],.]]],.]
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,[[.,[[[.,.],.],.]],.]],.]]],.]
[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[.,[[[[.,[.,.]],.],[.,.]],[[[.,.],.],.]]]],.]
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[[[.,[.,.]],.],[[[.,[.,.]],.],.]],.]]],.]
[1,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[[.,[.,.]],[[[.,.],.],[.,.]]],.],.]]],.]
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[[.,[[[.,[.,.]],.],.]],[.,.]],.],.]]],.]
[1,1,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[.,.]],[[.,.],[[[.,.],.],.]]]],.]],.]
[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[.,.]],[[.,[[[.,.],.],.]],.]]],.]],.]
[1,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[[[[[.,[.,.]],.],[.,.]],.],.]]],.]],.]
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[.,[.,.]],[[[.,.],.],.]]],.]],.]],.]
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[.,[[[.,[.,.]],.],.]],.]],.]],.]],.]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[[[.,.],.],[.,.]],[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[[[.,.],.],[.,.]],[[.,.],[[.,[[[.,.],.],.]],.]]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[[[[.,.],.],[.,.]],[[.,[[.,.],[[[.,.],.],.]]],.]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[[[[.,.],.],[.,.]],[[.,[[.,[[[.,.],.],.]],.]],.]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[[.,.],.],[[[[.,[.,.]],.],[.,.]],[[[.,.],.],.]]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[[.,.],.],[[[[.,[.,.]],.],[[[.,[.,.]],.],.]],.]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[[[.,.],.],[[[[.,[.,.]],[[[.,.],.],[.,.]]],.],.]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[[[.,.],.],[[[[.,[[[.,[.,.]],.],.]],[.,.]],.],.]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[[[[.,.],.],[[.,[.,.]],[[.,.],[[[.,.],.],.]]]],.]
[1,0,1,0,1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[[[[.,.],.],[[.,[.,.]],[[.,[[[.,.],.],.]],.]]],.]
[1,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[[[[.,.],.],[.,[[[[[.,[.,.]],.],[.,.]],.],.]]],.]
[1,0,1,0,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[[[[.,.],.],[[.,[[.,[.,.]],[[[.,.],.],.]]],.]],.]
[1,0,1,0,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[.,.],.],[[.,[[.,[[[.,[.,.]],.],.]],.]],.]],.]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[[.,.],[[[.,.],.],[.,.]]],[[.,.],[[[.,.],.],.]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[[.,.],[[[.,.],.],[.,.]]],[[.,[[[.,.],.],.]],.]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[[.,.],[[[[[[[.,.],.],[.,[.,.]]],.],[.,.]],.],.]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,.],[[[[.,.],.],[.,[.,.]]],[[[.,.],.],.]]],.]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[[[.,.],.],[[[.,[.,[.,.]]],.],.]],.]],.]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[[.,[[[.,.],.],.]],[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[[.,[[[.,.],.],.]],[.,.]],[[.,[[[.,.],.],.]],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[[.,[[[.,.],.],.]],[[[[[.,[.,.]],.],[.,.]],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,[[[.,.],.],.]],[[.,[.,.]],[[[.,.],.],.]]],.]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[[[.,[[[.,.],.],.]],[[.,[[[.,[.,.]],.],.]],.]],.]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],[[.,.],[[[.,.],.],[.,.]]]],[[[.,.],.],.]]
[1,0,1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[.,.],[[[.,.],.],[.,[.,.]]]],.],.]],.]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],[[.,[[[.,.],.],.]],[.,.]]],[[[.,.],.],.]]
[1,0,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[.,[[[.,.],.],.]],[.,[.,.]]],.],.]],.]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[[[[[.,.],.],[.,.]],.],[.,.]]],[[[.,.],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[.,[[[[[[[.,.],.],[.,.]],.],[.,[.,.]]],.],.]],.]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[.,[[.,.],[[[.,.],.],.]]],[.,.]],[[[.,.],.],.]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,[[.,.],[[[.,.],.],.]]],[[[.,[.,.]],.],.]],.]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[.,[[.,[[[.,.],.],.]],.]],[.,.]],[[[.,.],.],.]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,[[.,[[[.,.],.],.]],.]],[[[.,[.,.]],.],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[[[[.,.],[[.,.],[[.,.],[[[.,.],.],[.,.]]]]],.],.]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],[[.,.],[[.,[[[.,.],.],.]],[.,.]]]],.],.]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[[[[[.,.],.],[.,.]],.],[.,.]]]],.],.]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[[[[.,.],[[.,[[.,.],[[[.,.],.],.]]],[.,.]]],.],.]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[[.,.],[[.,[[.,[[[.,.],.],.]],.]],[.,.]]],.],.]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[[[[.,.],.],[.,.]],[[[.,.],.],[.,.]]]],.],.]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[[[.,.],.],[[[.,[.,.]],.],.]],[.,.]]],.],.]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[[[.,.],[[[.,.],.],[.,.]]],.],[.,.]]],.],.]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[[[.,[[[.,.],.],.]],[.,.]],.],[.,.]]],.],.]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[.,.],[[.,.],[[[.,.],.],.]]]],[.,.]],.],.]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[.,.],[[.,[[[.,.],.],.]],.]]],[.,.]],.],.]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[.,[[.,.],[[[.,.],.],.]]],.]],[.,.]],.],.]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[.,[[.,[[[.,.],.],.]],.]],.]],[.,.]],.],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[[[.,.],.],[.,.]]]]]]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,[[[.,.],.],.]],[.,.]]]]]
[1,0,1,1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[.,[[[[[.,.],.],[.,.]],.],[.,.]]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0,0]=>[[.,.],[[.,.],[[.,[[.,.],[[[.,.],.],.]]],[.,.]]]]
[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0,0]=>[[.,.],[[.,.],[[.,[[.,[[[.,.],.],.]],.]],[.,.]]]]
[1,0,1,1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[[.,.],[.,[[[[.,.],.],[.,.]],[[[.,.],.],[.,.]]]]]
[1,0,1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0,0]=>[[.,.],[.,[[[[.,.],.],[[[.,[.,.]],.],.]],[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[[[.,.],[[[.,.],.],[.,.]]],.],[.,.]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[[[.,[[[.,.],.],.]],[.,.]],.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0,0]=>[[.,.],[[.,[[.,.],[[.,.],[[[.,.],.],.]]]],[.,.]]]
[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,1,0,0,0]=>[[.,.],[[.,[[.,.],[[.,[[[.,.],.],.]],.]]],[.,.]]]
[1,0,1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0,0]=>[[.,.],[[.,[.,[[[[[.,.],.],[.,.]],.],.]]],[.,.]]]
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[[.,[[.,.],[[[.,.],.],.]]],.]],[.,.]]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[[.,[[.,[[[.,.],.],.]],.]],.]],[.,.]]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[.,[[[[.,.],.],[.,.]],[[.,.],[[[.,.],.],[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[.,[[[[.,.],.],[.,.]],[[.,[[[.,.],.],.]],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[.,[[[.,.],.],[[[[[.,[.,.]],.],[.,.]],.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[.,[[[[.,.],.],[[.,[.,.]],[[[.,.],.],.]]],[.,.]]]
[1,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[[[.,.],.],[[.,[[[.,[.,.]],.],.]],.]],[.,.]]]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[[[[[.,.],.],[.,[.,.]]],.],.]],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[.,[[[.,[[[.,.],.],.]],[.,.]],[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[.,[[[.,[[[.,.],.],.]],[[[.,[.,.]],.],.]],[.,.]]]
[1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[.,[[[[.,.],[[.,.],[[[.,.],.],[.,.]]]],.],[.,.]]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[[.,.],[[.,[[[.,.],.],.]],[.,.]]],.],[.,.]]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[[[[.,.],.],[.,.]],.],[.,.]]],.],[.,.]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[[[.,[[.,.],[[[.,.],.],.]]],[.,.]],.],[.,.]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[[[.,[[.,[[[.,.],.],.]],.]],[.,.]],.],[.,.]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0]=>[[.,[[.,.],[[.,.],[[.,.],[[[.,.],.],.]]]]],[.,.]]
[1,1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,1,0,0]=>[[.,[[.,.],[[.,.],[[.,[[[.,.],.],.]],.]]]],[.,.]]
[1,1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0]=>[[.,[[.,.],[.,[[[[[.,.],.],[.,.]],.],.]]]],[.,.]]
[1,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[[.,[[.,.],[[[.,.],.],.]]],.]]],[.,.]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[[.,[[.,[[[.,.],.],.]],.]],.]]],[.,.]]
[1,1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[[[.,.],.],[.,.]],[[[.,.],.],.]]]],[.,.]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[[[.,.],.],[[[.,[.,.]],.],.]],.]]],[.,.]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[[[.,.],[[[.,.],.],[.,.]]],.],.]]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[[[.,[[[.,.],.],.]],[.,.]],.],.]]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,.],[[.,.],[[[.,.],.],.]]]],.]],[.,.]]
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,.],[[.,[[[.,.],.],.]],.]]],.]],[.,.]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,[[[[[.,.],.],[.,.]],.],.]]],.]],[.,.]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,[[.,.],[[[.,.],.],.]]],.]],.]],[.,.]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,[[.,[[[.,.],.],.]],.]],.]],.]],[.,.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]],.]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.],.]]]
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[[[.,[.,.]],[[.,[.,.]],.]],.],.]]],.]]
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[[[.,[[.,[.,.]],.]],[.,.]],.],.]],.]]]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[[[.,[.,.]],[.,.]],[.,.]],.],.],.]]]]
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],[.,[[[.,[.,.]],.],.]]],.]],.]]
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[[.,[.,.]],[[.,[.,.]],[[.,.],.]]],.],.]]]
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,[[.,[.,.]],.]],[[.,[[.,.],.]],.]]],.]]
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],[.,.]],[.,[[[.,.],.],.]]]],.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[[[.,[[.,[.,.]],.]],.],[.,.]],.]],.]]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[[[.,[.,.]],[.,.]],.],[.,.]],.],.]]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[.,[.,[[[.,[.,.]],[[[.,[.,.]],.],[[.,.],.]]],.]]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[.,[.,[[.,[[.,[.,.]],.]],[[[.,.],[[.,.],.]],.]]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[[[.,[.,.]],[.,.]],[[.,.],[[[.,.],.],.]]]]]
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,[[.,[.,[[.,.],.]]],.]],.]],.]]
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[[.,[[.,[[.,.],[.,.]]],.]],.],.]]]
[1,1,1,0,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,1,0,0]=>[.,[[[.,[.,.]],[.,[[[[.,.],[.,[.,.]]],.],.]]],.]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0,0]=>[.,[[.,[.,.]],[[[.,[.,[[.,.],.]]],[[.,.],.]],.]]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,0,0]=>[.,[[.,[.,.]],[[.,[[.,.],[.,.]]],[[[.,.],.],.]]]]
[1,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,[.,.]],.],[.,[[.,[.,.]],.]]],.]],.]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[[[.,[.,.]],.],[[.,[.,.]],[.,.]]],.],.]]]
[1,1,1,0,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[[.,.],[.,[.,[[.,.],.]]]],.]],.]]
[1,1,1,0,0,1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[[[.,.],[.,[[.,.],[.,.]]]],.],.]]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,[[[.,[.,.]],.],.]],[[.,[.,.]],.]]],.]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],[[.,.],.]],[.,[[.,.],.]]]],.]]
[1,1,1,0,0,1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[.,[[[.,[.,.]],[.,[[[[.,.],.],[.,[.,.]]],.]]],.]]
[1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],.],[[.,.],[[.,[.,.]],.]]]],.]]
[1,1,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,.],[[.,.],[.,[[.,.],.]]]]],.]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[.,[[.,[[[.,[.,.]],.],.]],.]],[.,.]],.]]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[.,[.,[[.,[[[.,[.,.]],[[.,.],.]],.]],[[.,.],.]]]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[.,[.,.]],[[[.,[[.,.],.]],.],[.,.]]],.]]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[[[[[.,[.,.]],.],[.,.]],.],[.,.]],.]]]]
[1,1,1,1,0,0,1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[[.,[.,.]],[[[[.,.],[.,.]],.],[[.,.],.]]]]]
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,0,0]=>[.,[[.,[.,.]],[[[.,[.,[[[.,.],.],.]]],[.,.]],.]]]
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[.,[[.,[.,.]],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]]
[1,1,1,1,0,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[[.,[.,.]],.],[[.,[[.,.],.]],[.,.]]],.]]]
[1,1,1,0,0,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0,0]=>[.,[[.,[.,.]],[[[.,.],[.,[[[.,.],.],[.,.]]]],.]]]
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[[[[[.,[.,.]],.],.],[.,.]],[.,.]],.]]]]
[1,1,1,1,0,0,1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[[.,[.,.]],[[[[.,.],.],[.,.]],[[.,.],.]]]]]
[1,1,1,0,0,1,1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[.,[[.,[.,.]],[.,[[[[.,.],.],[[.,.],[.,.]]],.]]]]
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[.,[.,[[[.,[.,.]],.],[[.,.],[[[.,.],[.,.]],.]]]]]
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[.,[[.,[.,.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]],.]]
[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[.,[[.,.],[[[.,[[[.,[.,[.,.]]],[.,.]],.]],.],.]]]
[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[.,[[[.,.],[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]],.]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[[.,[[.,[.,[.,.]]],.]],[[.,.],.]],.]]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[.,[[.,.],[[[.,[.,[.,.]]],[.,.]],[[[.,.],.],.]]]]
[1,1,0,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[[[.,.],[.,[.,.]]],[[.,[.,[[.,.],.]]],.]],.]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[.,[[[.,.],[.,[.,.]]],[[[.,[[.,.],[.,.]]],.],.]]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[[.,.],[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]],.]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[[[.,.],[.,[.,.]]],[[.,.],[.,[[.,.],.]]]],.]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[.,[[.,.],[[[.,[[[.,[.,[.,.]]],.],.]],[.,.]],.]]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[.,[[.,.],[[[.,[.,[.,.]]],[[.,.],.]],[[.,.],.]]]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[[.,.],[.,[.,.]]],[[.,[[[.,.],.],[.,.]]],.]]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[.,[[.,.],[[[.,[.,[.,.]]],.],[[[.,.],[.,.]],.]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[[.,.],[.,[.,.]]],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[[.,[[.,[.,[.,.]]],.]],.]],.]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0,0]=>[.,[[.,[[.,.],.]],[[[[.,[.,[.,.]]],[.,.]],.],.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[[[.,[[.,.],.]],[.,[.,.]]],[.,[[.,.],.]]],.]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,[[.,.],.]],[[[[.,[.,[.,.]]],.],[.,.]],.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[[.,[[.,.],.]],[.,[.,.]]],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]],.]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[[.,.],[.,[.,[.,.]]]],[.,.]],.],.]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[[[.,.],[[.,.],[.,[.,.]]]],[.,[[.,.],.]]],.]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,.],[[[[[.,.],[.,[.,[.,.]]]],.],[.,.]],.]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[[.,.],[[.,.],[.,[.,.]]]],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[[.,[[.,[[.,.],.]],.]],[[.,[.,[.,.]]],.]],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[[.,[[.,[[.,.],.]],.]],[.,[.,.]]],[[.,.],.]]]
[1,1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[[.,.],[.,.]],.],[.,[.,[.,.]]]],.]],.]]
[1,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[[[.,.],[.,.]],.],[.,[.,.]]]],[[.,.],.]]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[[[.,.],[.,[[.,.],.]]],[[.,[.,[.,.]]],.]],.]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[[[.,.],[.,[[.,.],.]]],[.,[.,.]]],[[.,.],.]]]
[1,1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[[.,.],.],[.,.]],[.,[.,[.,.]]]],.]],.]]
[1,1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[[[.,.],.],[.,.]],[.,[.,.]]]],[[.,.],.]]]
[1,1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]],.]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0]=>[.,[[[.,.],[[.,.],[[.,.],[.,[.,.]]]]],[[.,.],.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[.,[[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,[.,.]]],.]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[[.,[[[.,.],[.,.]],.]],.],[.,[.,.]]]],.]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[.,[[[.,[[.,.],[[[.,[.,.]],.],.]]],[.,[.,.]]],.]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[[.,[[.,.],.]],[[.,.],.]],[.,[.,.]]]],.]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[[[.,.],[.,.]],[[[.,.],.],[.,[.,.]]]]],.]]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[.,[[[[.,.],[[.,[.,[[.,.],.]]],.]],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[[.,.],[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]],.]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[.,[[[.,[[[.,.],.],[[.,[.,.]],.]]],[.,[.,.]]],.]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0,0]=>[.,[[[[.,.],[[.,.],[.,[[.,.],.]]]],[.,[.,.]]],.]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[[.,[[[.,.],.],.]],[.,.]],[.,[.,.]]]],.]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[[[.,.],[[.,.],.]],[[.,.],[.,[.,.]]]]],.]]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[[.,.],[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]],.]]
[1,1,1,0,1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[[[.,.],.],[[[.,.],[.,.]],[.,[.,.]]]]],.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]],.]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[.,.]]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[.,[[.,[[[.,.],[.,.]],.]],.]],.],[.,.]]]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[[[[.,.],[[.,[.,.]],.]],.],.]]],[.,.]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[[[[.,[[.,.],.]],[.,.]],.],.]],[.,.]]]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[[[[.,.],[.,.]],[.,.]],.],.],[.,.]]]]]
[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[[.,.],[.,[[[.,[.,.]],.],.]]],.]],[.,.]]]
[1,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[[.,.],[[.,[.,.]],[[.,.],.]]],.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],[.,.]]]
[1,1,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0,0]=>[.,[[.,[[[.,.],[.,.]],[.,[[[.,.],.],.]]]],[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[[[[.,[[.,.],.]],.],[.,.]],.]],[.,.]]]]
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[[[[.,.],[.,.]],.],[.,.]],.],[.,.]]]]]
[1,1,1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[.,[.,[[[.,.],[[[.,[.,.]],.],[[.,.],.]]],[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[.,[.,[[.,[[.,.],.]],[[[.,.],[[.,.],.]],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[[[.,.],[.,.]],[[.,.],[[[.,.],.],[.,.]]]]]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,[[.,[.,[[.,.],.]]],.]],.]],[.,.]]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]]]
[1,1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,1,1,0,0,0]=>[.,[[[.,.],[.,[[[[.,.],[.,[.,.]]],.],.]]],[.,.]]]
[1,1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[.,[[.,.],[[[.,[.,[[.,.],.]]],[[.,.],.]],[.,.]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[.,[[.,.],[[.,[[.,.],[.,.]]],[[[.,.],.],[.,.]]]]]
[1,1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[[[.,.],.],[.,[[.,[.,.]],.]]],.]],[.,.]]]
[1,1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[[[.,.],.],[[.,[.,.]],[.,.]]],.],[.,.]]]]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[[[.,.],[.,[.,[[.,.],.]]]],.]],[.,.]]]
[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[[[.,.],[.,[[.,.],[.,.]]]],.],[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[.,[[[.,.],.],.]],[[.,[.,.]],.]]],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[.,[[.,[[[.,.],[[.,.],.]],[.,[[.,.],.]]]],[.,.]]]
[1,1,0,1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0,1,1,0,0,0]=>[.,[[[.,.],[.,[[[[.,.],.],[.,[.,.]]],.]]],[.,.]]]
[1,1,1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0]=>[.,[[.,[[[.,.],.],[[.,.],[[.,[.,.]],.]]]],[.,.]]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,.],[[.,.],[.,[[.,.],.]]]]],[.,.]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[.,[[.,[[[.,.],.],.]],.]],[.,.]],[.,.]]]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[[.,[[[.,.],[[.,.],.]],.]],[[.,.],[.,.]]]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[.,[.,[[[.,.],[[[.,[[.,.],.]],.],[.,.]]],[.,.]]]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[[[[.,.],.],[.,.]],.],[.,.]],[.,.]]]]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[[[[.,.],[.,.]],.],[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0,0,0]=>[.,[[.,.],[[[.,[.,[[[.,.],.],.]]],[.,.]],[.,.]]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,0,0]=>[.,[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0,0]=>[.,[.,[[[[.,.],.],[[.,[[.,.],.]],[.,.]]],[.,.]]]]
[1,1,0,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,0,0]=>[.,[[.,.],[[[.,.],[.,[[[.,.],.],[.,.]]]],[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[[[[.,.],.],.],[.,.]],[.,.]],[.,.]]]]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[[[[.,.],.],[.,.]],[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,0]=>[.,[[.,.],[.,[[[[.,.],.],[[.,.],[.,.]]],[.,.]]]]]
[1,1,1,0,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[.,[.,[[[.,.],.],[[.,.],[[[.,.],[.,.]],[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]]]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[[.,.],[[[.,[.,.]],.],.]],.],.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[[.,[.,.]],[.,[[[[.,.],[.,.]],.],[[[.,.],.],.]]]]
[1,1,0,0,1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0]=>[[.,[.,.]],[.,[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[[.,[[.,[[.,.],.]],.]],.],.]],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,[[.,.],.]],[[[.,.],.],.]]],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[[.,[.,.]],[[[.,.],.],[[.,.],[[[.,[.,.]],.],.]]]]
[1,1,0,0,1,1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[.,[.,.]],[[[[.,.],.],[.,[[.,[[.,.],.]],.]]],.]]
[1,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[[.,.],[.,[[.,.],[[.,.],.]]]],.],.]]
[1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,[[.,[[[.,.],.],[.,.]]],.]],.],.]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[[.,[[[.,.],.],.]],[[.,.],.]]]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,[.,.]],[[.,.],[[[.,.],.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[[[.,[[[.,.],.],.]],.],[.,.]],.]]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[[[.,.],.],[[[.,.],.],[.,.]]],.]]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[.,[.,[[[.,[.,.]],[.,[.,.]]],[[[.,[.,.]],.],.]]]]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,[.,.]],[[.,[[.,[.,[.,.]]],.]],.]]],.]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[[[[.,[[.,[.,.]],[.,.]]],.],[[.,.],.]],.],.]]
[1,1,1,1,0,0,1,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[.,[.,.]],[[[.,[.,[.,.]]],.],[.,.]]],.]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[.,[[[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]],.],.]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[[.,[[.,[.,.]],.]],.],[.,.]],.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[.,[[[[[.,[.,.]],.],[[[.,.],[.,[.,.]]],.]],.],.]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[[.,[.,.]],.],[[.,.],[.,.]]],.],[[.,.],.]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[.,[.,[[[.,[.,.]],[[[.,[.,.]],.],[.,[.,.]]]],.]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,[.,[[.,[[.,[.,.]],.]],.]]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[[[.,[.,.]],.],[[.,.],.]],.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0]=>[.,[[.,[.,.]],[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[.,[[[.,[.,.]],.],[.,.]]],[.,[.,.]]],.]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[[.,[.,.]],[[[.,[.,.]],.],.]],.],.]]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[.,[[[[.,[.,.]],[.,.]],.],[[[.,.],.],.]]]],.]
[1,1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]]]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,[[.,[[.,[.,.]],.]],.]],.],.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[.,[.,.]],.]],[[[.,.],.],.]]],.]],.]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[[.,[[[.,[.,.]],.],[[.,.],[[[.,[.,.]],.],.]]]],.]
[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[[.,[[[[.,[.,.]],.],[.,[[.,[[.,.],.]],.]]],.]],.]
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0,1,0]=>[[.,[[[[.,[.,.]],[.,[[.,.],[[.,.],.]]]],.],.]],.]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[[.,[[[.,[.,.]],.],[.,.]]],.]],.],.]],.]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,[[[.,.],.],.]],[[.,.],.]]]],.]
[1,1,1,0,0,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[[.,[[.,[.,.]],[[[.,.],.],[[.,.],[[.,.],.]]]]],.]
[1,1,1,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]]]],.]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[[[.,[[[.,[.,.]],.],.]],.],[.,.]],.]]],.]
[1,1,1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[[[.,[.,.]],.],[[[.,.],.],[.,.]]],.]]],.]
[1,0,1,0,1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[[[[.,.],.],[.,.]],[.,[[.,.],[[[.,[.,.]],.],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[[.,.],.],[.,.]],[[.,[.,[[.,[[.,.],.]],.]]],.]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[[[.,.],.],[.,.]],[[[[[.,.],.],[[.,.],.]],.],.]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[[.,.],.],[.,.]],[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[[[[.,.],.],[.,.]],[.,[[.,[[[.,.],.],[.,.]]],.]]]
[1,0,1,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[[[.,.],.],[[[.,[[[.,[.,.]],[.,[.,.]]],.]],.],.]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[[[.,.],.],[[[.,[[.,[.,.]],[.,.]]],.],[[.,.],.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[.,.],.],[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[[.,.],.],[[[.,[.,.]],.],[[[.,.],[.,[.,.]]],.]]]
[1,0,1,0,1,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[[[[.,.],.],[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]],.]
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[[[[.,.],.],[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]],.]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[[.,.],.],[[[[[.,[.,.]],.],[[.,.],.]],.],.]],.]
[1,0,1,0,1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[[[[.,.],.],[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]],.]
[1,0,1,0,1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[[[[.,.],.],[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]],.]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[[.,.],[.,[[.,.],[.,.]]]],[[[.,[[.,.],.]],.],.]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[[.,.],[.,[[.,.],[.,.]]]],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,0,0]=>[[.,.],[.,[[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]],.]]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[[.,[[[.,.],[.,[.,[.,.]]]],.]],.],.]],.]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[[[.,.],[[[.,[[.,.],[.,[.,.]]]],.],[[.,.],.]]],.]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[[.,[.,[[.,.],.]]],[.,.]],[[[.,[[.,.],.]],.],.]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[[.,[.,[[.,.],.]]],[.,.]],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[[.,[.,[[.,.],.]]],[.,[[[.,[.,.]],[.,[.,.]]],.]]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[[[.,[.,[[.,.],.]]],[[[.,[[.,[.,.]],.]],.],.]],.]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[[[.,[.,[[.,.],.]]],[[[.,[.,.]],.],[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],[[[.,[[.,.],.]],.],[.,.]]],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[.,.],[[[.,[[.,.],.]],.],[[.,[.,[.,.]]],.]]],.]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],[[[.,.],.],[[.,.],[.,.]]]],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[[[.,.],[[[.,.],.],[[[.,.],[.,[.,[.,.]]]],.]]],.]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]],[.,[[.,.],.]]]
[1,1,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]],.]]],.]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,[[[.,[[.,.],.]],.],.]],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[[.,[[[.,[[.,.],.]],.],.]],[.,[[.,[.,.]],.]]],.]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,[[[.,.],.],[[.,.],.]]],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[[.,[[[.,.],.],[[.,.],.]]],[.,[[.,[.,.]],.]]],.]
[1,0,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]],.],.]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[[[[.,.],[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]],.],.]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[[.,.],[[[[[.,.],.],[[.,.],.]],.],[.,.]]],.],.]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0]=>[[[[.,.],[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]],.],.]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]],.],.]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[[.,[[[.,.],[.,[.,.]]],.]],.],[.,.]]],.],.]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]],.],.]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[[[.,[[.,.],.]],.],[[.,[.,.]],[.,.]]]],.],.]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[[[.,.],.],[[[.,.],[.,[.,.]]],[.,.]]]],.],.]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[.,[[.,.],[[[.,[.,.]],.],.]]]],[.,.]],.],.]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[.,[.,[[.,[[.,.],.]],.]]],.]],[.,.]],.],.]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[[[[.,.],.],[[.,.],.]],.],.]],[.,.]],.],.]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[.,.],[.,[[.,.],[[.,.],.]]]]],[.,.]],.],.]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[.,[[.,[[[.,.],.],[.,.]]],.]]],[.,.]],.],.]
[1,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[[[.,.],[[[.,[.,.]],.],.]],.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[[.,.],[.,[[[[.,.],[.,.]],.],[[[.,.],.],[.,.]]]]]
[1,0,1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[[[.,[[.,[[.,.],.]],.]],.],.]],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],[[[.,.],.],.]]],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[[.,.],[[[.,.],.],[[.,.],[[[.,[.,.]],.],[.,.]]]]]
[1,0,1,1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0]=>[[.,.],[[[[.,.],.],[.,[[.,[[.,.],.]],.]]],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[[.,.],[.,[[.,.],[[.,.],.]]]],.],[.,.]]]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,[[.,[[[.,.],.],[.,.]]],.]],.],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[[.,[[[.,.],.],.]],[[.,.],[.,.]]]]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[.,.],[[.,.],[[[.,.],.],[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[[.,.],[.,[[[[.,[[[.,.],.],.]],.],[.,.]],[.,.]]]]
[1,0,1,1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[[.,.],[.,[[[[.,.],.],[[[.,.],.],[.,.]]],[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[[[.,.],[.,[.,.]]],[[[.,[.,.]],.],[.,.]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]],[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[[[.,[[.,.],[.,.]]],.],[[.,.],.]],.],[.,.]]]
[1,1,1,0,1,1,0,0,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[.,[[.,[[.,.],[.,.]]],[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[.,[.,[[[.,.],[[[.,[.,[.,.]]],.],[.,.]]],[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[[[.,[[.,.],.]],.],[[.,[.,.]],.]],.],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[[[.,[[.,.],.]],.],[.,.]],.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[[[.,.],.],[[[.,.],[.,[.,.]]],.]],.],[.,.]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[[[.,.],.],[[.,.],[.,.]]],.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[.,[.,[[[.,.],[[[.,[.,.]],.],[.,[.,.]]]],[.,.]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[.,[[.,[.,[[.,[[.,.],.]],.]]],[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[.,[[[[[.,.],.],[[.,.],.]],.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[.,[[.,.],[[.,[[.,.],[[.,.],[.,[.,.]]]]],[.,.]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[.,[.,[[[.,[[[.,.],.],[.,.]]],[.,[.,.]]],[.,.]]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[[[.,.],[[[.,[.,.]],.],.]],.],.]]],[.,.]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[[[.,.],[.,.]],.],[[[.,.],.],.]]]],[.,.]]
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]]],[.,.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[[.,[[.,[[.,.],.]],.]],.],.]],.]],[.,.]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],[[[.,.],.],.]]],.]],[.,.]]
[1,1,0,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0]=>[[.,[[[.,.],.],[[.,.],[[[.,[.,.]],.],.]]]],[.,.]]
[1,1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[[[.,.],.],[.,[[.,[[.,.],.]],.]]],.]],[.,.]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[[.,.],[.,[[.,.],[[.,.],.]]]],.],.]],[.,.]]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[.,[[.,[[[.,.],.],[.,.]]],.]],.],.]],[.,.]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[[.,[[.,.],[[.,[[[.,.],.],.]],[[.,.],.]]]],[.,.]]
[1,1,0,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[[.,[[.,.],[[[.,.],.],[[.,.],[[.,.],.]]]]],[.,.]]
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[[[.,[[[.,.],.],.]],.],[.,.]],.]]],[.,.]]
[1,1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[[[.,.],.],[[[.,.],.],[.,.]]],.]]],[.,.]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[[[.,[.,[.,.]]],.],[.,.]],.],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[[.,[[.,.],[.,.]]],[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[[[.,[.,.]],.],[[.,[.,.]],.]],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[[.,[[[.,.],.],[.,.]]],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[[.,[[.,.],.]],[[.,[.,.]],.]],[.,[.,[.,.]]]],.]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]],[.,.]],.],.]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[[[.,[.,.]],.],[[[.,[.,.]],.],.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[[[.,[.,[.,.]]],.],[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]],[.,.]],.]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,[[[.,.],.],[.,.]]],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]],[.,.]],.]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,[[.,.],[.,.]]],[[[.,.],.],.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[[.,[[.,[.,.]],.]],[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[[[.,[.,.]],.],[.,[[.,.],.]]],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[[[.,[[.,[.,[.,[.,.]]]],.]],[.,[[.,.],.]]],.],.]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[[.,[.,.]],.],[[.,.],[[.,.],.]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,[[[.,[.,[.,[.,.]]]],.],.]],[.,[[.,.],.]]],.]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,[[.,.],.]],[[.,.],[[.,.],.]]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,[.,[[[.,.],[.,[.,.]]],.]]],.],[.,[.,.]]],.]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[[.,.],[[[.,.],[.,[.,.]]],.]]],[.,[.,.]]],.]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[[[.,[.,[[.,[.,[.,.]]],.]]],.],[.,[[.,.],.]]],.]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,[[.,.],[[.,[.,[.,.]]],.]]],[.,[[.,.],.]]],.]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[[.,[.,[.,.]]],.],[[[[.,.],[.,.]],.],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[[.,[.,[[.,[.,[.,.]]],.]]],.],[[[.,[.,.]],.],.]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[[.,[.,[.,.]]],.],[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,[.,[[[.,[.,[.,.]]],.],.]]],.],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[[.,[.,[[.,.],.]]],.],[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[[[[[.,.],[.,.]],.],[.,.]],.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[[[[.,[.,.]],.],.],[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[[.,.],[[.,[.,[.,.]]],.]],[.,.]],.]],[.,.]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[.,[[[.,[.,.]],.],[.,.]]],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]],[[.,.],.]]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[[[[.,.],[.,.]],.],[[.,.],.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[.,[[[.,[.,.]],.],.]],[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[.,.],[[[.,[.,[.,.]]],.],.]],[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[[[.,.],[[.,.],.]],[[.,.],.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[[.,[.,.]],.],[.,[.,.]]],.]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[.,[[.,[[.,.],.]],[.,.]]],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[.,[[.,.],.]],[.,[.,.]]],.]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[[.,[[[.,.],.],.]],[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0]=>[[[[[.,[.,.]],.],[.,[.,[[.,[.,.]],.]]]],.],[.,.]]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[[[[.,[[.,[.,.]],.]],[.,[.,[[.,[.,.]],.]]]],.],.]
[1,1,0,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[[[[.,[.,.]],.],[[.,.],[.,[[.,[.,.]],.]]]],[.,.]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[.,[[[.,[.,.]],.],.]],[.,[.,[[.,[.,.]],.]]]],.]
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[[.,.],[.,[[.,[.,.]],.]]]],[.,.]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[[.,[.,[[.,.],.]]],.],[.,[.,[[.,[.,.]],.]]]],.]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[.,[[.,.],[[.,.],.]]],[.,[.,[[.,[.,.]],.]]]],.]
[1,1,1,0,0,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[.,[.,[.,.]]],.],[[[.,.],[.,[[.,[.,.]],.]]],.]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[.,[.,[[.,.],.]]],.],[[.,[.,[[.,[.,.]],.]]],.]]
[1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[[.,[[[[.,.],[.,.]],.],[.,[[.,[.,.]],.]]]],[.,.]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[.,[[[.,[.,.]],.],.]],[[.,[.,[[.,[.,.]],.]]],.]]
[1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[[.,[[[.,.],[[.,.],.]],[.,[[.,[.,.]],.]]]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[.,[.,[[.,[.,.]],.]]],.],.]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]],[[.,.],.]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]],.],[.,.]],.]
[1,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]],[.,.]],.]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]],.],[[.,.],.]]
[1,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],[.,[[[.,[.,.]],.],[.,.]]]],.]],[.,.]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]],.],[.,.]],.]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]],[.,.]],.]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]],.],[[.,.],.]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],[.,[[.,[[.,.],.]],[.,.]]]],.]],[.,.]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]],[[.,.],.]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[[[.,[.,.]],.],[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[[.,[[.,.],.]],[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]]
[1,1,0,0,1,0,1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[[[.,[.,.]],.],[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[[.,[[.,.],.]],[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0,0]=>[[[.,[.,.]],.],[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0,0]=>[[.,[[.,.],.]],[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[[[.,[.,.]],.],[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[[.,[[.,.],.]],[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[.,[.,.]],.],[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[[.,[[.,.],.]],[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[[[[.,[.,.]],.],[.,[.,.]]],.],[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[[.,[[.,[.,.]],.]],[.,[.,.]]],.],.]]],.]
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[[[.,[.,.]],.],[[.,.],[.,.]]],[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[[.,[[[.,[.,.]],.],.]],[.,[.,.]]],.]]],.]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[[.,[[.,.],.]],[[.,.],[.,.]]],[.,.]]]],.]
[1,1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[[[.,[.,[[.,.],.]]],.],[.,[.,.]]],.]]],.]
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[[.,[[.,.],[[.,.],.]]],[.,[.,.]]],.]]],.]
[1,1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[[.,[.,[[[.,[.,[.,.]]],.],[[[.,.],[.,.]],.]]]],.]
[1,1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[[.,[.,[[[.,[.,[[.,.],.]]],.],[[.,[.,.]],.]]]],.]
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[.,[[[[.,.],[.,.]],.],[.,.]]],[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[[.,[.,[[.,[[[.,[.,.]],.],.]],[[.,[.,.]],.]]]],.]
[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[.,[[[.,.],[[.,.],.]],[.,.]]],[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[[.,[.,[[.,[[.,[.,.]],.]],[[[.,[.,.]],.],.]]]],.]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[.,[[.,[[.,[[.,.],.]],[.,.]]],[[.,.],.]]]],.]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[[[[[.,[.,[.,.]]],.],[.,.]],.],[.,[.,.]]],.]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[[.,[[.,.],[.,.]]],[.,.]],.],.],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[.,[[[[[.,[.,.]],.],[[.,[.,.]],.]],[.,[.,.]]],.]]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[.,[[[.,.],.],[.,.]]],[.,.]],.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[.,[[[[.,[[.,.],.]],[[.,[.,.]],.]],[.,[.,.]]],.]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[[[.,[.,[.,.]]],.],[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[.,[[.,[[.,.],[.,.]]],[.,.]]],[.,.]],.],.]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[.,[[[[.,[.,.]],.],[[[.,[.,.]],.],.]],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[[[.,[.,[.,.]]],.],[[.,.],.]],[[.,.],[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[[[.,[.,[.,.]]],.],[.,.]],.]],[.,.]],.]]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[.,[[[.,[[[.,.],.],[.,.]]],[[.,.],.]],[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[[.,[[.,.],[.,.]]],[.,.]],.]],[.,.]],.]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[.,[[[.,[[.,.],[.,.]]],[[[.,.],.],.]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,[[.,[.,.]],.]],[[.,.],.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[[.,[.,.]],.],[.,[[.,.],.]]],.],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[[.,[[.,[.,[.,.]]],.]],[.,[[.,.],.]]],.],.]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[.,[[[[.,[.,.]],.],[[.,.],[[.,.],.]]],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,[[[.,[.,[.,.]]],.],.]],[.,[[.,.],.]]],.]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[.,[[[.,[[.,.],.]],[[.,.],[[.,.],.]]],[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[[[.,[.,[[[.,.],[.,.]],.]]],.],[.,[.,.]]],.]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[.,[[[.,[[.,.],[[[.,.],[.,.]],.]]],[.,[.,.]]],.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[[[.,[.,[[.,[.,.]],.]]],.],[.,[[.,.],.]]],.]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,[[.,.],[[.,[.,.]],.]]],[.,[[.,.],.]]],.]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[.,[[[.,[.,[.,.]]],.],[[[[.,.],[.,.]],.],[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[.,[[[.,[.,[[.,[.,.]],.]]],.],[[[.,[.,.]],.],.]]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[.,[[[.,[.,[.,.]]],.],[[[.,.],[[.,.],.]],[.,.]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,[.,[[[.,[.,.]],.],.]]],.],[[.,[.,.]],.]]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[.,[[[.,[.,[[.,.],.]]],.],[[.,[[.,.],.]],[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[.,[[.,[[[[[.,.],[.,.]],.],[.,.]],.]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[.,[[[[.,[.,.]],.],.],[.,.]]],[[.,.],[.,.]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[[[.,.],[[.,[.,.]],.]],[.,.]],.]],[.,.]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[.,[[.,[[[.,[.,.]],.],[.,.]]],[[[.,.],.],[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,.],.]]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[.,[[.,[[[[.,.],[.,.]],.],[[.,.],.]]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[.,[[.,[[[.,[.,.]],.],.]],[[.,[[.,.],.]],[.,.]]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[[.,.],[[[.,[.,.]],.],.]],[.,.]]],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[.,[[.,[[[.,.],[[.,.],.]],[[.,.],.]]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,[[.,[.,.]],.]],[[[[.,[.,.]],.],[.,.]],.]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[.,[[.,[[.,[[.,.],.]],[.,.]]],[[[.,.],.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[.,[[.,[[.,[.,.]],.]],[[[.,[[.,.],.]],[.,.]],.]]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[.,[[.,[[[.,.],.],.]],[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,[.,.]],.]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]],.]
[1,0,1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[[[.,.],.],[[.,.],[[.,.],[.,[[[.,.],[.,.]],.]]]]]
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[[[.,.],.],[[.,.],[.,[[[.,.],[[.,.],[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[.,.],.],[[.,[[.,.],.]],[.,[[[.,.],[.,.]],.]]]]
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[[[.,.],.],[.,[[[.,.],[[.,.],[[.,.],[.,.]]]],.]]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[[[[.,.],.],.],[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[.,.],.],[.,[[[.,[[.,.],.]],[[.,.],[.,.]]],.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[[[[.,.],.],[[.,.],[[.,.],.]]],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[[[[.,.],.],[[.,.],.]],[.,.]],[.,[[.,[.,.]],.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[.,.],[[.,.],.]],[[.,.],[.,[[[.,.],[.,.]],.]]]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[.,.],[[.,.],.]],[.,[[[.,.],[[.,.],[.,.]]],.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[[[.,.],[[.,.],.]],[[.,.],.]],[.,[[.,[.,.]],.]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[[.,.],[[.,.],[[.,.],.]]],[.,[[[.,.],[.,.]],.]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[[.,.],[[.,[[.,.],.]],.]],[.,[[[.,.],[.,.]],.]]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[[[.,.],.],[[[.,.],[[.,.],[[.,.],[.,[.,.]]]]],.]]
[1,0,1,0,1,0,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[[[[.,.],.],.],[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[.,.],.],[[[.,[[.,.],.]],[[.,.],[.,[.,.]]]],.]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[[[[.,.],.],.],[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[[[[.,.],.],.],[.,.]],[[.,[[.,[.,.]],[.,.]]],.]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[.,.],[[.,.],.]],[[[.,.],[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[[.,.],[[.,.],.]],.],[[[.,[.,.]],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[[.,.],[[.,.],[[.,.],.]]],[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[[.,.],[[.,[[.,.],.]],.]],[[[.,.],[.,[.,.]]],.]]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[[[[.,.],.],.],[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[[[[[.,.],.],.],[.,[[.,[.,.]],.]]],[[.,[.,.]],.]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[[[.,.],[[.,.],.]],.],[[[.,[.,[.,.]]],[.,.]],.]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[[[.,.],.],.],[[.,[.,[.,.]]],.]],[[.,[.,.]],.]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[[[[.,.],.],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[.,[[.,.],.]],.],[[.,.],[.,[[[.,.],[.,.]],.]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[.,[[.,.],.]],.],[.,[[[.,.],[[.,.],[.,.]]],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[[[.,[[.,.],.]],.],[[.,.],.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[[.,[[.,.],.]],[[.,.],.]],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[.,[[.,.],.]],.],[[[.,.],[[.,.],[.,[.,.]]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[[.,[[.,.],.]],.],.],[[[.,[.,.]],[.,[.,.]]],.]]
[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]=>[[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],[.,[.,.]]],.]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[[[.,.],.],[.,[[[.,.],[.,.]],.]]],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[[.,.],[[.,[[.,.],.]],[[.,.],.]]],[.,[.,.]]],.]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[[[[.,.],[[.,.],[[.,.],.]]],[.,.]],[.,[.,.]]],.]
[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]=>[[[[.,[[.,.],.]],.],[.,[[[.,.],[.,.]],[.,.]]]],.]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],[.,.]]]],.]
[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]=>[[[[.,[[.,[[.,.],.]],.]],[[.,.],.]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],[.,.]]],.]
[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]=>[[[[.,.],[.,[[.,.],[[.,.],[[.,.],.]]]]],[.,.]],.]
[1,0,1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[[[.,.],.],[[.,.],[[.,[.,.]],[.,.]]]],[.,.]],.]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,[[.,[[.,.],.]],[[.,.],.]]]],[.,.]],.]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[[[.,.],.],[.,[[[.,.],[.,[.,.]]],.]]],[.,.]],.]
[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]=>[[[[.,[[.,.],.]],[.,[[.,.],[[.,.],.]]]],[.,.]],.]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[[[.,[[.,.],.]],.],[.,[[.,[.,.]],.]]],[.,.]],.]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[[.,[[.,.],[[.,.],.]]],[.,[[.,.],.]]],[.,.]],.]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[[.,[[.,[[.,.],.]],.]],[.,[[.,.],.]]],[.,.]],.]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0,1,0]=>[[[[[.,.],.],[[[.,.],[.,[.,[.,.]]]],.]],[.,.]],.]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[[.,.],.],[.,[[.,[.,.]],.]]],[.,.]],[.,.]],.]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[[[[[.,[[.,.],.]],.],[[.,[.,[.,.]]],.]],[.,.]],.]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[[.,.],.],[[.,[.,[.,.]]],.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[[.,.],[[.,.],[[.,.],.]]]],[.,.]],[[.,.],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[[.,.],[[.,[[.,.],.]],.]]],[.,.]],[[.,.],.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[[.,[[.,.],.]],[[.,.],.]]],[.,.]],[[.,.],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[[.,[[.,.],[[.,.],.]]],.]],[.,.]],[[.,.],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,.]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]]
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,[[.,.],.]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[[[.,.],[.,.]],[.,.]],[.,[[.,.],.]]],[[.,.],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,[[.,.],[[.,.],.]]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,[[.,[[.,.],.]],.]],.]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[[.,.],[.,.]],[.,[[.,.],.]]],[.,.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],[[.,[[.,.],.]],.]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[[.,.],[.,.]],[.,[[.,.],[[.,.],.]]]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[[[.,.],[.,.]],[.,[[.,[[.,.],.]],.]]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[.,.],[.,.]],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]
[1,0,1,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[.,.],[.,.]],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,.],[.,.]],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]
[1,0,1,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[[.,.],[.,[[.,.],.]]],[.,.]],[.,.]],[[.,.],.]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[[.,.],[.,[[.,.],.]]],[.,.]],[[.,[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[[.,.],[.,[[.,.],.]]],[.,[[.,.],.]]],[[.,.],.]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,.],[.,[[.,.],.]]],[[.,[[.,.],[[.,.],.]]],.]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[.,.],[.,[[.,.],.]]],[[.,[[.,[[.,.],.]],.]],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,.],[.,[[.,.],[[.,.],.]]]],[.,.]],[[.,.],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,.],[.,[[.,.],[[.,.],.]]]],[[.,[[.,.],.]],.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,.],[.,[[.,[[.,.],.]],.]]],[.,.]],[[.,.],.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,.],[.,[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],.]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[[.,.],[[.,.],[[.,.],.]]]]],[[.,.],.]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[[.,.],[[.,[[.,.],.]],.]]]],[[.,.],.]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[[.,[[.,.],.]],[[.,.],.]]]],[[.,.],.]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[[.,[[.,.],[[.,.],.]]],.]]],[[.,.],.]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[[.,[[.,[[.,.],.]],.]],.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[[.,[[.,.],.]],[.,.]],[.,[[.,.],.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,[[.,.],.]],[.,.]],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[.,[[.,.],.]],[.,.]],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,[[.,.],.]],[.,[[.,.],.]]],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],[[.,[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[.,[[.,.],.]],[.,[[.,.],[[.,.],.]]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,[[.,.],.]],[.,[[.,[[.,.],.]],.]]],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,[[.,.],[[.,.],.]]],[.,.]],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,[[.,.],[[.,.],.]]],[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,[[.,.],[[.,.],.]]],[.,[[.,.],.]]],[[.,.],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,[[.,[[.,.],.]],.]],[.,.]],[.,.]],[[.,.],.]]
[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 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")
Weight
26
Created
Jan 29, 2020 at 13:25 by FindStatCrew
Updated
Jan 29, 2020 at 13:25 by Martin Rubey
searching the database
Sorry, this map was not found in the database.