- FindStat

Identifier
Mp00034: Dyck paths —to binary tree: up step, left tree, down step, right tree⟶ Binary trees
Mp00016: Binary trees —left-right symmetry⟶ Binary trees
Images
=>
            
              Cc0005;cc-rep-0Cc0010;cc-rep-1Cc0010;cc-rep-2
            

            [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]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[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]=>[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[[[[[[[.,[[.,.],.]],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[[[[[[.,[.,[.,.]]],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[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]=>[.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[.,[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]],.]
[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]=>[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[[[[[[[.,[.,[.,.]]],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[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]=>[[[[[[.,[.,.]],[.,.]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[[.,[[[[.,.],.],.],.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[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]=>[.,[[[[[[.,.],[[.,.],.]],.],.],.],.]]=>[[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]],.]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[.,[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0]=>[[[[[[[[.,.],.],.],[.,.]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[[[[[[[.,.],.],.],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]=>[[[[[[.,.],[.,[.,.]]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[.,[[[[[.,.],.],.],.],.]],.],[.,.]]=>[[.,.],[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[.,[[[[[[[.,.],.],.],.],[.,.]],.],.]]=>[[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]]=>[[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]],.]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[.,[[[[[[.,.],[.,[.,.]]],.],.],.],.]]=>[[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0]=>[[[[[[.,.],.],[[.,.],.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[[[.,.],.],.],.]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]=>[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[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]=>[.,[[[[[[[.,.],.],.],.],.],[.,.]],.]]=>[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[.,[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]]=>[[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.]
[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]=>[.,[[[[[.,[.,[.,[.,.]]]],.],.],.],.]]=>[[.,[.,[.,[.,[[[[.,.],.],.],.]]]]],.]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]=>[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[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]=>[[[[[[.,[.,.]],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]]=>[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[.,[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]],.]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]
[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]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[.,[[[[[[.,[.,.]],.],.],.],.],[.,.]]]=>[[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[.,[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]]=>[[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[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]=>[[[[[.,[[.,.],.]],.],.],.],[[.,.],.]]=>[[.,[.,.]],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]=>[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]=>[[[[[[[.,[.,.]],.],.],.],.],.],[[.,.],.]]=>[[.,[.,.]],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0]=>[[[[[[.,.],[.,.]],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[[.,.],[.,.]]]]]]
[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]=>[[[[.,[[[.,.],.],.]],.],.],[[.,.],.]]=>[[.,[.,.]],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[.,[[[[.,[[.,[.,.]],.]],[.,.]],.],.]]=>[[.,[.,[[.,.],[[.,[[.,.],.]],.]]]],.]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[.,[[[[[.,.],[.,[.,[.,.]]]],.],.],.]]=>[[.,[.,[.,[[[[.,.],.],.],[.,.]]]]],.]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]=>[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]
[]=>.=>.
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[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]=>[[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]=>[.,[[[[[[[.,.],.],[.,.]],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]],.]=>[.,[[[[[[.,.],[[.,.],.]],.],.],.],.]]
[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]=>[[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]],.]=>[.,[[[[[.,[[.,[.,.]],.]],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]],.]=>[.,[[[[[.,[[.,.],[.,.]]],.],.],.],.]]
[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]=>[[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]],.]=>[.,[[[[[[[.,.],.],.],[.,.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]],.]=>[.,[[[[.,[[[[.,.],.],.],.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[.,[.,[.,[[.,[[[.,.],.],.]],.]]]],.]=>[.,[[[[.,[[.,[.,[.,.]]],.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]],.]=>[.,[[[[.,[[[.,.],.],[.,.]]],.],.],.]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]],.]=>[.,[[[[.,[.,[[[.,.],.],.]]],.],.],.]]
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[.,[.,[[[[[.,.],.],.],.],.]]]],.]=>[.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]],.]=>[.,[[[[[[[.,.],.],.],.],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]],.]=>[.,[[[.,[[[[[.,.],.],.],.],.]],.],.]]
[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]=>[[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],[.,[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]],.]=>[.,[[[.,[[[[.,.],.],.],[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]],.]=>[.,[[[.,[[.,.],[[[.,.],.],.]]],.],.]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,[.,[[[[[.,.],.],.],.],[.,.]]]],.]=>[.,[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]]
[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]=>[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]=>[.,[[[[[[[.,.],.],.],.],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[[.,.],[[[[[.,.],.],.],.],.]]],.]=>[.,[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]],.]=>[.,[[[.,.],[[[[[.,.],.],.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]=>[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]],.]=>[.,[[.,[[.,[[[[.,.],.],.],.]],.]],.]]
[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]=>[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]=>[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,[[.,[[[[[.,.],.],.],.],.]],.]],.]=>[.,[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[[[.,.],[.,.]],[[.,[.,.]],.]]],.]=>[.,[[[.,[[.,.],.]],[[.,.],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]],.]=>[.,[[.,[[[[[.,.],.],.],.],[.,.]]],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]],.]=>[.,[[.,[[[[.,.],.],.],[[.,.],.]]],.]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]],.]=>[.,[[.,[[[.,.],.],[[[.,.],.],.]]],.]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]],.]=>[.,[[.,[.,[[[[[.,.],.],.],.],.]]],.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[[.,[[[[.,.],.],.],[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],[.,[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[[.,[[[[[.,.],.],.],.],[[.,.],.]]],.]=>[.,[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]]
[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]=>[[.,[[[[[[.,.],.],.],.],[.,.]],.]],.]=>[.,[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]
[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]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[[.,.],[[.,.],[[.,.],[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],[.,.]],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[.,.],[[.,.],[[.,[[.,.],.]],.]]],.]=>[.,[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[[.,.],[[.,[[.,[[.,.],.]],.]],.]],.]=>[.,[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[[.,.],[[[[[.,.],.],.],.],[.,.]]],.]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],[.,.]],[[.,.],.]]]
[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]=>[[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]],.]=>[.,[[[.,[[.,.],.]],.],[[[.,.],.],.]]]
[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]=>[[[.,[.,[.,[.,[[[.,.],.],.]]]]],.],.]=>[.,[.,[[[[[.,[.,[.,.]]],.],.],.],.]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[[.,[[.,.],.]],.],.]]]
[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]=>[[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.],.]=>[.,[.,[[[[[[.,.],.],.],.],[.,.]],.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[[.,[[.,.],.]],.]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]],.]=>[.,[[.,.],[[.,[[[[.,.],.],.],.]],.]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.]=>[.,[.,[[.,[[[[[.,.],.],.],.],.]],.]]]
[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]=>[[[.,[[.,[[.,[.,[.,.]]],.]],.]],.],.]=>[.,[.,[[.,[[.,[[[.,.],.],.]],.]],.]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[[[.,[[[.,.],.],.]],[.,[[.,.],.]]],.]=>[.,[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]]
[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]=>[[[.,[[[.,.],[.,.]],.]],[[.,.],.]],.]=>[.,[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[[[.,[[[[.,.],.],.],.]],[[.,.],.]],.]=>[.,[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[[[.,[[[[[.,.],.],.],.],[.,.]]],.],.]=>[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[[[[.,.],.],[[.,.],[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[[[[.,.],.],[[[[[.,.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[[[[.,.],[.,.]],[[.,.],[[.,.],.]]],.]=>[.,[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[[[[.,.],[.,.]],[[[[.,.],.],.],.]],.]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]=>[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[[[[.,.],[[[[.,.],.],.],[.,.]]],.],.]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[[.,.],[[[[[.,.],.],.],.],.]],.],.]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[[[[.,[.,[.,.]]],[.,.]],[[.,.],.]],.]=>[.,[[.,[.,.]],[[.,.],[[[.,.],.],.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.],.]=>[.,[.,[[[[.,.],.],.],[[[.,.],.],.]]]]
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[[[[.,[.,[.,.]]],[[[.,.],.],.]],.],.]=>[.,[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.],.]=>[.,[.,[[[.,.],.],[[[[.,.],.],.],.]]]]
[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]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[[[[.,[.,[[.,[.,[.,.]]],.]]],.],.],.]=>[.,[.,[.,[[[.,[[[.,.],.],.]],.],.]]]]
[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]=>[[[[.,[.,[[[[.,.],.],.],.]]],.],.],.]=>[.,[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[[[[.,[[.,[.,[.,.]]],.]],[.,.]],.],.]=>[.,[.,[[.,.],[[.,[[[.,.],.],.]],.]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[.,[[.,[.,[.,[.,.]]]],.]],.],.],.]=>[.,[.,[.,[[.,[[[[.,.],.],.],.]],.]]]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[[[.,[[[.,.],[.,.]],.]],[.,.]],.],.]=>[.,[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[[[[.,[[[.,[.,.]],.],.]],.],[.,.]],.]=>[.,[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[[[[.,[[[[.,.],.],.],[.,.]]],.],.],.]=>[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]
[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]=>[[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[[[[[.,.],.],.],[[[[.,.],.],.],.]],.]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0]=>[[[[[.,.],.],[.,.]],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]=>[[[[[.,.],.],[.,[.,[.,[.,.]]]]],.],.]=>[.,[.,[[[[[.,.],.],.],.],[.,[.,.]]]]]
[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]=>[[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.]=>[.,[.,[.,[[[[[.,.],.],.],.],[.,.]]]]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0]=>[[[[[.,.],[[[.,.],.],[.,.]]],.],.],.]=>[.,[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,0]=>[[[[[.,[.,.]],.],.],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0]=>[[[[[.,[.,.]],.],[.,[.,[.,.]]]],.],.]=>[.,[.,[[[[.,.],.],.],[.,[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[[[[[.,[.,.]],[.,[.,[.,.]]]],.],.],.]=>[.,[.,[.,[[[[.,.],.],.],[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0]=>[[[[[.,[.,[.,.]]],.],[.,[.,.]]],.],.]=>[.,[.,[[[.,.],.],[.,[[[.,.],.],.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0]=>[[[[[.,[.,[.,.]]],[.,[.,.]]],.],.],.]=>[.,[.,[.,[[[.,.],.],[[[.,.],.],.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[[[[[.,[.,[.,[.,.]]]],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[[[[.,.],.],.],.]]]]]
[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]=>[[[[[.,[.,[[.,.],[.,.]]]],.],.],.],.]=>[.,[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]]
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[[[[[.,[.,[[[.,.],.],.]]],.],.],.],.]=>[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]]
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[.,[[.,[.,[.,.]]],.]],.],.],.],.]=>[.,[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[[[[[.,[[[.,.],.],[.,.]]],.],.],.],.]=>[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]
[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]=>[[[[[[.,.],.],.],.],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0]=>[[[[[[.,.],.],.],.],[[.,.],[.,.]]],.]=>[.,[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[[[[[[.,.],.],.],.],[[[.,.],.],.]],.]=>[.,[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0]=>[[[[[[.,.],[.,.]],[[.,.],.]],.],.],.]=>[.,[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[[[[[[.,.],[.,[.,[.,.]]]],.],.],.],.]=>[.,[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]=>[[[[[[.,.],[[.,.],[.,.]]],.],.],.],.]=>[.,[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[[[[[[.,.],[[[.,.],.],.]],.],.],.],.]=>[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]=>[[[[[[.,[.,.]],.],.],.],[[.,.],.]],.]=>[.,[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0]=>[[[[[[.,[.,.]],.],[[.,.],.]],.],.],.]=>[.,[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[[[[[[.,[.,.]],[.,.]],[.,.]],.],.],.]=>[.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[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]=>[[[[[[.,[[.,.],.]],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0]=>[[[[[[.,[[.,.],.]],[.,.]],.],.],.],.]=>[.,[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]]
[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]=>[[[[[[[.,.],.],.],.],[[.,.],.]],.],.]=>[.,[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[[[[[[[.,.],.],[.,[.,.]]],.],.],.],.]=>[.,[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]]
[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]=>[[[[[[[.,.],[.,.]],.],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.]=>[.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]
[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]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]=>[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]=>[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]=>[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]=>[[[[[[[.,[[[.,.],.],.]],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]=>[[[[[.,[[[.,.],.],[.,.]]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]=>[[[[[[.,[[[[.,.],.],.],.]],.],.],.],.],.]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]=>[[[[.,[[[[.,.],.],.],[.,.]]],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]=>[[[[[.,[[[[[.,.],.],.],.],.]],.],.],.],.]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]=>[[[.,[[[[[.,.],.],.],.],[.,.]]],.],.]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]=>[[[[.,[[[[[[.,.],.],.],.],.],.]],.],.],.]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]=>[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]=>[[[.,[[[[[[[.,.],.],.],.],.],.],.]],.],.]
[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]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]=>[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]=>[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]=>[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]=>[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[.,[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]]=>[[[[[.,[[.,.],[.,[.,.]]]],.],.],.],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]
[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]=>[.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]]=>[[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]]=>[[[[[.,[.,[[[.,.],.],.]]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]=>[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[.,[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]]=>[[[[[.,[.,[[.,[.,.]],.]]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]=>[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[.,[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[.,[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]]]=>[[[[[[.,[.,[[[.,.],.],.]]],.],.],.],.],.]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]]=>[[[[.,[.,[[[[.,.],.],.],.]]],.],.],.]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]=>[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[.,[.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]]=>[[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.],.]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[.,[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]]=>[[[.,[[.,.],[[.,[[.,.],.]],.]]],.],.]
[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]=>[[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]]=>[[[.,[.,[[[[[.,.],.],.],.],.]]],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]]=>[[.,[[.,.],[[[[[.,.],.],.],.],.]]],.]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[.,[.,[[[[[.,.],[.,.]],.],[.,.]],.]]]=>[[[.,[[.,.],[.,[[.,.],[.,.]]]]],.],.]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[.,[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]]=>[[.,[.,[[[[[[.,.],.],.],.],.],.]]],.]
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]=>[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[[.,[[[.,.],[.,.]],.]],[.,.]],.]]=>[[.,[[.,.],[[.,[[.,.],[.,.]]],.]]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[.,[[[[[[.,.],.],.],.],[.,[.,.]]],.]]=>[[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]]=>[[.,[.,[.,[[[[[.,.],.],.],.],.]]]],.]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]]]=>[[[.,[.,[[[[[[.,.],.],.],.],.],.]]],.],.]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]=>[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]]
[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]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.]=>[.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]],.]=>[.,[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[[[.,[[.,[.,[.,[.,[.,.]]]]],.]],[.,.]],.]=>[.,[[.,.],[[.,[[[[[.,.],.],.],.],.]],.]]]
[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]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]],.]=>[.,[[.,.],[.,[[[[[[.,.],.],.],.],.],.]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]
[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]=>[.,[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]]=>[[[[[[[.,[.,.]],.],[.,.]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]]=>[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[.,[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]]=>[[[[[[[.,.],.],[.,[.,.]]],.],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]=>[[[[[[.,[.,.]],[.,.]],[.,.]],.],.],.]
[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]=>[.,[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],[.,[.,.]]],.],.],.]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[.,[.,[.,[[[.,.],.],[[[.,.],.],.]]]]]=>[[[[[.,[.,[.,.]]],[.,[.,.]]],.],.],.]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[.,[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]=>[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]
[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]=>[.,[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]]=>[[[[[[.,[.,[.,.]]],.],.],.],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[.,[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]
[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]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[.,[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[.,[[[[[.,.],.],.],.],[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]
[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]=>[[.,.],[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[[[[[.,.],.],.],.],.]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],[.,.]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],[.,.]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[.,[[[[[[.,.],.],.],.],.],.]]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[.,.],[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],[.,.]],[.,.]],[.,.]]
[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]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[[[[[.,.],.],.],.],.]]]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[.,.],[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[.,.],[[[[.,.],.],.],[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],[.,.]]
[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]=>[[[.,.],.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[[[[[[.,[.,.]],.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[.,.],.],[.,[.,[.,[[[.,.],.],.]]]]]=>[[[[[.,[.,[.,.]]],.],.],.],[.,[.,.]]]
[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]=>[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[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]=>[[[[.,.],.],.],[.,[.,[.,[[.,.],.]]]]]=>[[[[[.,[.,.]],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,.],.],.],[.,[[[.,.],.],[.,.]]]]=>[[[[.,.],[.,[.,.]]],.],[.,[.,[.,.]]]]
[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]=>[[[[.,.],.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[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]=>[[[[[.,.],.],.],.],[.,[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[[[[[.,.],.],.],.],[.,[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],.],[.,[.,[.,[.,.]]]]]
[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]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]=>[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]
[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]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]=>[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[.,[.,[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]]]=>[[[[[[[.,.],[.,[.,[.,.]]]],.],.],.],.],.]
[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]=>[.,[.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]]=>[[[[[[[.,[.,.]],[.,.]],[.,.]],.],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]=>[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[.,[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[.,[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]=>[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[.,[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]]]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[.,[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[.,[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[.,[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[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]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]
[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]=>[[.,.],[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,.],[.,[[[[[[[.,.],.],.],.],.],.],.]]]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]]=>[[[[[[.,.],.],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[[[.,.],.],.],.]]]]=>[[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[.,.],[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[.,.],[[[[.,.],.],.],[[[[.,.],.],.],.]]]=>[[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]],[.,.]]
[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]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[.,.],.],[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,[.,.]]]
[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]=>[[[[.,.],.],.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[[[[[[.,[.,.]],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],.],.],[[.,.],[[.,.],[[.,.],.]]]]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[[.,.],.],.],[[.,.],[[[[.,.],.],.],.]]]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[[.,.],.],.],[[[[.,.],.],.],[[.,.],.]]]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,.],.],.],.],[.,[.,[.,[[.,.],.]]]]]=>[[[[[.,[.,.]],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[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]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]
[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]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[.,[.,.]],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[.,[.,.]],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]]=>[[[.,.],.],[[[[[.,[.,.]],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]=>[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.],.]=>[.,[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]
[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]=>[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[[[[[[[.,[[.,.],.]],.],.],.],.],.],[.,.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]]=>[[[[[[.,[[.,.],.]],.],.],.],[.,.]],.]
[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]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[[.,.],.]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,[.,.]]]]]]
[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]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[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]=>[[[.,[[[[[[[.,.],.],.],.],.],.],.]],.],.]=>[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],[.,.]]=>[[.,.],[[.,[[[[[.,.],.],.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.]=>[.,[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,[.,.]],.],[[[[[.,.],.],.],.],.]]=>[[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[[[[[.,[.,.]],.],.],.],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[.,[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],[[.,.],.]],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[.,[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]]=>[[[[[[[.,.],[[[.,.],.],.]],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[.,[.,[.,[.,.]]]],[.,[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],.],[[[[.,.],.],.],.]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[.,.],[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],[[.,.],.]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.]=>[.,[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]]=>[[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]],.]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]]=>[[.,[.,[[[[[.,.],.],.],.],[.,.]]]],.]
[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]=>[[.,[.,[.,[.,[.,.]]]]],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.]=>[.,[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,[.,.]]]],[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]],.]=>[.,[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]],.]=>[.,[[[[[.,[.,[[[.,.],.],.]]],.],.],.],.]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]],.]=>[.,[[[.,[.,[[[[[.,.],.],.],.],.]]],.],.]]
[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]=>[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[[.,[[[[[.,.],.],.],.],.]],.]]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],[.,.]]
[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]=>[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[[[[[.,.],.],.],.],[[[.,[.,.]],.],.]]=>[[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]]
[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]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[[.,.],.],[[[[[.,[.,.]],.],.],.],.]]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]]
[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]=>[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[[[[[[.,.],.],.],.],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[.,.],[[[[[[.,.],.],.],[.,.]],.],.]]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]=>[[[[[[.,.],[[[.,.],.],.]],.],.],.],.]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[.,.],[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[[[[.,[[[[.,.],.],.],.]],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]],.]=>[.,[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]],.]=>[.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[[.,[[.,.],[[.,.],.]]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]]=>[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]=>[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],[.,.]]=>[[.,.],[[[[[.,.],[.,.]],[.,.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,.],[.,.]]],[[[.,.],[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[.,[[.,.],[[.,.],[.,.]]]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[[[.,.],[.,.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[.,[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],.]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[.,[[[.,.],[.,.]],[[.,.],[[.,.],.]]]]=>[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],.]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],.]]
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]],.]=>[.,[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]]
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]],.]=>[.,[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]],.]=>[.,[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]],.]=>[.,[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[.,[[.,[.,[.,.]]],.]]]=>[[[.,[[[.,.],.],.]],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]],.]=>[.,[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]],.]=>[.,[[[[[[.,[[[.,.],.],.]],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]],.]=>[.,[[[[.,[[[[[.,.],.],.],.],.]],.],.],.]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]],.]=>[.,[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]],.]=>[.,[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]],.]=>[.,[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]],.]=>[.,[[[[[[[.,[[[.,.],.],.]],.],.],.],.],.],.]]
[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]=>[[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]],.]=>[.,[[[[.,[[[[[[.,.],.],.],.],.],.]],.],.],.]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]],.]=>[.,[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]],.]=>[.,[[[.,[[[[[[[.,.],.],.],.],.],.],.]],.],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]],.]=>[.,[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.],.]=>[.,[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[[[[[[[[.,.],[[.,.],.]],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[[[[[[[[.,.],.],[[.,.],.]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],.]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]]
[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]=>[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]
[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]=>[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]
[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]=>[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]]=>[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]],.]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]]=>[[.,[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]],.]
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]],.]
[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]=>[.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>[[.,[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]],.]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]]=>[[.,[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]],.]
[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]=>[.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]],.]
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],[[.,.],.]]
[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]=>[[.,[.,.]],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[[[.,[.,.]],[.,.]],.]]=>[[.,[[.,.],[[.,.],.]]],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],[[.,.],.]]],.]]
[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]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[.,.],[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],[.,.]]=>[[.,.],[.,[[[[[[[.,.],.],.],.],.],.],.]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],[.,.]]=>[[.,.],[.,[.,[[[[[.,.],.],.],.],.]]]]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]=>[[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]]
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[[.,[[[[[.,.],.],.],.],.]],.]]]=>[[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.]
[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]=>[[[.,.],.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[[.,[[[[[.,.],.],.],.],.]],[.,[.,.]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]]
[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[.,[[[[[.,[.,[.,[.,.]]]],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[[[[.,.],.],.],.]]]]],.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]=>[[[[[.,[.,.]],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[.,[.,.]],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0]=>[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.]=>[.,[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[.,[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]]=>[[[.,[[[[[.,.],.],.],[.,.]],.]],.],.]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]],.]=>[.,[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],[[.,.],.]],.]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[[.,[[[[[[[.,.],.],.],.],.],.],.]],[.,.]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.],.]=>[.,[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]=>[[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]],.]=>[.,[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]=>[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[[[[[.,.],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]]=>[[[.,[.,.]],[[[[[.,.],.],.],.],.]],.]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[[.,.],.]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]=>[[.,.],[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[.,.],[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,.],[[[[[[.,.],.],.],.],[.,.]],.]]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]
[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[.,[.,[[[[[[.,.],.],.],.],.],.]]],.],.]=>[.,[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]]]
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[.,[.,.]]],[[[[[.,.],.],.],.],.]]=>[[.,[.,[.,[.,[.,.]]]]],[[[.,.],.],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.]=>[.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[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]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[.,[.,[[.,[[[[.,.],.],.],.]],[.,.]]]]=>[[[[.,.],[[.,[.,[.,[.,.]]]],.]],.],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],[.,.]]=>[[.,.],[[[[[[.,.],[.,.]],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],[.,.]]]=>[[[.,.],[[.,.],.]],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],[.,.]]=>[[.,.],[[[[[.,[.,[.,.]]],.],.],.],.]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[[[[[[.,[.,[.,[.,.]]]],[.,.]],.],.],.],.]=>[.,[.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0]=>[[[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]=>[[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[.,.],[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[[[[[[.,.],[[.,.],.]],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[.,[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]]=>[[[[[.,[[.,[[.,.],.]],.]],.],.],.],.]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]]=>[[.,[[.,[[[[[.,.],.],.],.],.]],.]],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]=>[[.,[.,.]],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0]=>[[[[[.,.],.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[[.,[.,[[[[[.,.],.],.],.],.]]],.],.],.]=>[.,[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[[.,[[[.,[[.,.],.]],[.,.]],.]],[.,.]]=>[[.,.],[[.,[[.,.],[[.,[.,.]],.]]],.]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[.,[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],[[.,.],[.,.]]],.]
[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]=>[.,[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]]=>[[[[[.,.],.],[[[.,.],.],[.,.]]],.],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[.,.],[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]]=>[[[[[.,.],[[.,.],.]],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,.]],.],[[.,.],[[.,.],[[.,.],.]]]]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[[[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.],.]=>[.,[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[[[[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.],.],.]=>[.,[.,[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]]]]
[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]=>[[[[.,[[[.,[.,[.,[.,.]]]],.],.]],.],.],.]=>[.,[.,[.,[[.,[.,[[[[.,.],.],.],.]]],.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[[.,.],.]],[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[.,[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]]=>[[[[[.,[[[.,.],[.,.]],.]],.],.],.],.]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0]=>[[[[[[.,.],.],[.,.]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]],.]=>[.,[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[.,.],[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[[[[[.,[[[.,.],.],.]],.],.],.],[.,.]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[.,[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],[[.,[.,.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0]=>[[[[[.,.],[.,.]],.],.],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[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]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,[.,.]]]=>[[[.,.],.],[[[[[.,.],.],[.,.]],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[.,[.,[.,[.,.]]]],.]]=>[[.,[[[[.,.],.],.],.]],[[[.,.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[.,[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]]=>[[[[[[[.,[[.,[.,.]],.]],.],.],.],.],.],.]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[[[[[.,[.,[.,[[.,[.,.]],.]]]],.],.],.],.]=>[.,[.,[.,[.,[[[[.,[[.,.],.]],.],.],.]]]]]
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[.,[.,[[.,[.,[.,.]]],.]]],.],.],.],.]=>[.,[.,[.,[.,[[[.,[[[.,.],.],.]],.],.]]]]]
[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]=>[[[[[.,[[.,[.,[.,[.,.]]]],.]],.],.],.],.]=>[.,[.,[.,[.,[[.,[[[[.,.],.],.],.]],.]]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[.,[.,.]],[[.,[.,.]],[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],[[.,.],.]],[[.,.],.]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[.,.],[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],[[.,.],.]],.],[.,.]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]]=>[[[[.,.],[[[[.,.],.],.],[.,.]]],.],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[.,[[[[[[.,.],.],.],.],[[.,.],.]],.]]=>[[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]],.]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0]=>[[[[[[[.,.],[.,.]],.],.],.],.],[[.,.],.]]=>[[.,[.,.]],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],[[.,.],.]],[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],.]]]]=>[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],.]],[.,.]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.]=>[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]=>[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[.,.],[.,[.,.]]],.]]],[.,.]]=>[[.,.],[[[.,[[[.,.],.],[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[.,[.,[[[.,.],.],.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,[.,[.,.]]],.],.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[.,[.,[.,[[.,[.,.]],.]]]],[.,[.,.]]]=>[[[.,.],.],[[[[.,[[.,.],.]],.],.],.]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[.,.],[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[.,[.,[.,.]]],[.,[.,[.,[[.,.],.]]]]]=>[[[[[.,[.,.]],.],.],.],[[[.,.],.],.]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],[.,.]]]]=>[[[[.,.],[[[.,.],.],.]],.],[[.,.],.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]]=>[[[[.,.],[[[[[.,.],.],.],.],.]],.],.]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,.],[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]]=>[[[[.,.],[[[[[.,.],.],.],.],.]],.],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[[[.,.],.],.],.],.]]]
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]=>[[[[[[[.,.],[[[.,.],.],.]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0]=>[[[[[[.,.],.],.],.],[[.,.],.]],[.,.]]=>[[.,.],[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[.,[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]]=>[[[[[[.,.],[[.,.],[.,.]]],.],.],.],.]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[.,[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]]=>[[[[[.,.],[.,[[.,.],[.,.]]]],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[.,[.,[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]]]=>[[[[[[[.,.],[[.,.],[.,.]]],.],.],.],.],.]
[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0]=>[[[[[[.,.],.],[[[[.,.],.],.],.]],.],.],.]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]],.]=>[.,[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]]=>[[.,[[[[[[.,.],[.,.]],.],.],.],.]],.]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[.,.],[[[[[.,.],.],.],.],.]],[.,.]]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[[.,.],[[[[[[.,.],.],.],.],.],.]],.],.]=>[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[[[.,.],.],.]],[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[[[.,.],[[[[[.,.],.],.],.],.]],[.,.]]
[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]=>[[[[[[[[.,[.,.]],.],[.,.]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]=>[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[.,.],[[[.,[[.,.],.]],[.,.]],.]]]=>[[[.,[[.,.],[[.,[.,.]],.]]],[.,.]],.]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],.]]=>[[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],.]],.]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],[.,.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]=>[[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]],.]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[.,[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]]=>[[[[.,[.,[[[.,.],.],[.,.]]]],.],.],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[[.,.],.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[[.,[.,.]],.]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]]=>[[.,[[[[[[.,.],.],.],.],[.,.]],.]],.]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[.,.],[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[[[[[.,[.,[[.,.],.]]],.],.],.],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,[.,.]]]=>[[[.,.],.],[[[[.,.],.],.],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]]=>[[[.,[[[[[.,.],.],.],.],.]],[.,.]],.]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[.,[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]]=>[[[[.,[[[[.,.],.],.],.]],[.,.]],.],.]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[.,[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]]=>[[[[[.,[[[.,.],.],.]],[.,.]],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[.,[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]]=>[[[[[[.,[[.,.],.]],[.,.]],.],.],.],.]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],[.,.]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]]=>[[[[.,.],.],[[[[[.,.],.],.],.],.]],.]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[.,.]],[[.,[[.,[[.,.],.]],.]],.]]=>[[.,[[.,[[.,[.,.]],.]],.]],[[.,.],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]=>[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]=>[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]=>[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,.],[.,[[.,[[.,.],.]],.]]],.]]=>[[.,[[[.,[[.,[.,.]],.]],.],[.,.]]],.]
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]],.]=>[.,[[[.,[[.,[[.,[[.,.],.]],.]],.]],.],.]]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.],.]=>[.,[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],[.,.]]=>[[.,.],[[[[[[[.,[.,.]],.],.],.],.],.],.]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,[[.,.],.]],.],[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],[.,[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[[.,.],.]],[[[[[.,.],.],.],.],.]]=>[[.,[.,[.,[.,[.,.]]]]],[[.,[.,.]],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[.,[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]]=>[[[[[.,[[[.,[.,.]],.],.]],.],.],.],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[.,[[.,[.,.]],.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,[[.,.],.]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]],.]=>[.,[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[.,[[[.,.],[[.,.],[[.,.],.]]],.]]]=>[[[.,[[[.,[.,.]],[.,.]],[.,.]]],.],.]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[.,[[.,.],[[.,.],[[[.,.],[[.,.],.]],.]]]]=>[[[[.,[[.,[.,.]],[.,.]]],[.,.]],[.,.]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[[[.,.],.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[.,[[.,.],.]],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[.,[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]]=>[[[[[.,[.,.]],[[.,.],[.,.]]],.],.],.]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[.,[.,[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]]]=>[[[[[[.,[.,.]],[[.,.],[.,.]]],.],.],.],.]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[.,[.,[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]]]=>[[[[[[.,.],[.,.]],[[.,.],[.,.]]],.],.],.]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]],.]=>[.,[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[.,[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]]=>[[[.,.],[.,[[[[[.,.],.],.],.],.]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]=>[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],[[.,.],.]]=>[[.,[.,.]],[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[.,.]],[[[.,.],[.,.]],[[.,.],.]]]=>[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],.]=>[.,[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]]=>[[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]],.]=>[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],[.,.]]]=>[[[.,.],[[[.,.],.],.]],[[[.,.],.],.]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],[.,.]]]=>[[[.,.],[[[[.,.],.],.],.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[[[.,.],[[[[.,.],.],.],[.,.]]],[.,.]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[[[.,.],[[[[[.,.],.],.],.],.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,.],[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]]=>[[[.,.],[[[[[.,.],.],.],.],[.,.]]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[.,[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[[.,.],.]]]]],[[.,.],.]]=>[[.,[.,.]],[[[[[.,[.,.]],.],.],.],.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[[.,.],.]]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[.,[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],[.,[[.,.],.]]],.]
[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[[.,.],.],[[.,.],.]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],.],[[.,.],.]],[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[[.,.],[[.,.],.]],.]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.],.]=>[.,[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[[.,.],[.,.]],.],[[[.,.],.],[.,.]]]=>[[[.,.],[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[[.,.],.]]=>[[.,[.,.]],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]=>[[.,[.,.]],[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]=>[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[.,[[[[[.,[.,.]],.],[.,.]],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[[.,.],[.,[[.,.],.]]]]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]]=>[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.]
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]]=>[[[.,.],[.,[[.,[[[.,.],[.,.]],.]],.]]],.]
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]]=>[[.,[[[.,.],[.,[[[.,.],[.,.]],.]]],.]],.]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[.,[[[.,.],[.,.]],.]]]],.]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]]=>[[.,[[.,[[[.,.],[[.,.],[.,.]]],.]],.]],.]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]=>[[[.,.],[.,[[[.,.],[[.,.],[.,.]]],.]]],.]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]]=>[[.,[[[.,.],[[.,.],[[.,.],[.,.]]]],.]],.]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.]
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[.,[[[[[[.,[.,.]],.],[.,.]],[.,.]],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[[.,.],[[.,.],[.,[[.,.],.]]]]]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[.,[[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]],.]]=>[[.,[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.]],.]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0]=>[.,[[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.],[.,.]]]=>[[[.,.],[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]]],.]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0]=>[.,[[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]],.]]=>[[.,[[[.,.],[.,[[.,[[[.,.],[.,.]],.]],.]]],.]],.]
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0,1,0]=>[.,[[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[.,[[.,[[[.,.],[.,.]],.]],.]]]],.]
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0]=>[.,[[.,[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]],.]]=>[[.,[[.,[[[.,.],[.,[[[.,.],[.,.]],.]]],.]],.]],.]
[1,0,1,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0,1,0]=>[.,[[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.],[.,.]]]=>[[[.,.],[.,[[[.,.],[.,[[[.,.],[.,.]],.]]],.]]],.]
[1,0,1,1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]],.]]=>[[.,[[[.,.],[[.,.],[.,[[[.,.],[.,.]],.]]]],.]],.]
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[.,[[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[[.,.],[.,[[[.,.],[.,.]],.]]]]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[.,[[.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]],.]]=>[[.,[[.,[[.,[[[.,.],[[.,.],[.,.]]],.]],.]],.]],.]
[1,0,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0]=>[.,[[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.],[.,.]]]=>[[[.,.],[.,[[.,[[[.,.],[[.,.],[.,.]]],.]],.]]],.]
[1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.]]=>[[.,[[[.,.],[.,[[[.,.],[[.,.],[.,.]]],.]]],.]],.]
[1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[.,[[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[.,[[[.,.],[[.,.],[.,.]]],.]]]],.]
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[.,[[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]],.]]=>[[.,[[.,[[[.,.],[[.,.],[[.,.],[.,.]]]],.]],.]],.]
[1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[.,[[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.],[.,.]]]=>[[[.,.],[.,[[[.,.],[[.,.],[[.,.],[.,.]]]],.]]],.]
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]],.]]=>[[.,[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.]],.]
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[.,[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]=>[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[.,.],[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[[[.,.],[[[[.,.],.],[.,.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[.,.],[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],[[[.,.],[.,.]],.]],[.,.]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,.],[.,[[.,.],.]]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[[.,[.,.]],.],[.,.]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],.],[[[.,.],.],.]],[.,[.,.]]]=>[[[.,.],.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[[[[[[.,[[.,[[.,.],.]],.]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[[.,[.,.]],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,[.,.]]]=>[[[.,.],.],[[[[[.,.],.],.],[.,.]],.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[.,.]],[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[[[.,[[.,.],[[.,.],[[.,.],.]]]],[.,.]],.]=>[.,[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],.]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[[.,.],[.,.]],[[.,.],.]]],.]]=>[[.,[[[.,[.,.]],[[.,.],[.,.]]],.]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[[.,.],[.,.]],[[[.,.],[[.,.],.]],.]]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[.,[[[.,[[.,[[.,[[.,.],.]],.]],.]],.],.]]=>[[.,[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]],.]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[.,[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]]=>[[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],.]
[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]=>[[.,[[[.,[[.,.],.]],[[.,[.,.]],.]],.]],.]=>[.,[[.,[[.,[[.,.],.]],[[.,[.,.]],.]]],.]]
[1,1,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[[.,[[.,[[[.,.],[[.,[.,.]],.]],.]],.]],.]=>[.,[[.,[[.,[[.,[[.,.],.]],[.,.]]],.]],.]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[[.,[[.,[[.,[[[.,[.,.]],.],.]],.]],.]],.]=>[.,[[.,[[.,[[.,[.,[[.,.],.]]],.]],.]],.]]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[.,[[.,[[.,.],.]],.]],[.,.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,.],[[.,[[.,[.,.]],.]],.]]]]]
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,1,0,0]=>[[[[.,[[[.,[[.,.],.]],[.,.]],.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,[[.,.],[[.,[.,.]],.]]],.]]]]
[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]=>[[.,[[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]],.]],.]=>[.,[[.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]],.]]
[1,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0,1,0,0]=>[[[[.,[[.,[[[.,.],[.,.]],.]],.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,[[.,[[.,.],[.,.]]],.]],.]]]]
[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]=>[[.,[[[[.,[[[.,.],[.,.]],.]],[.,.]],[.,.]],.]],.]=>[.,[[.,[[.,.],[[.,.],[[.,[[.,.],[.,.]]],.]]]],.]]
[1,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0,0]=>[[[.,[[.,[[[[.,.],[.,.]],[.,.]],.]],.]],[.,.]],.]=>[.,[[.,.],[[.,[[.,[[.,.],[[.,.],[.,.]]]],.]],.]]]
[1,1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,0]=>[[.,[[[.,[[[[.,.],[.,.]],[.,.]],.]],[.,.]],.]],.]=>[.,[[.,[[.,.],[[.,[[.,.],[[.,.],[.,.]]]],.]]],.]]
[1,1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0]=>[[.,[[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],.]],.]],.]=>[.,[[.,[[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],.]],.]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[.,.]],[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],[[.,[.,.]],[.,.]]]=>[[[.,.],[[.,.],.]],[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[[.,[[.,[.,.]],.]],.],[[.,[[.,[.,.]],.]],.]],.]=>[.,[[.,[[.,[[.,.],.]],.]],[.,[[.,[[.,.],.]],.]]]]
[1,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[[[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]]]]
[1,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,0,1,0,0]=>[[[.,[[[.,[[.,[[.,.],.]],.]],[.,.]],.]],[.,.]],.]=>[.,[[.,.],[[.,[[.,.],[[.,[[.,[.,.]],.]],.]]],.]]]
[1,1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,0,0]=>[[.,[[[[.,[[.,[[.,.],.]],.]],[.,.]],[.,.]],.]],.]=>[.,[[.,[[.,.],[[.,.],[[.,[[.,[.,.]],.]],.]]]],.]]
[1,1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[[[.,[[.,[[[.,[[.,.],.]],[.,.]],.]],.]],[.,.]],.]=>[.,[[.,.],[[.,[[.,[[.,.],[[.,[.,.]],.]]],.]],.]]]
[1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0]=>[[.,[[[.,[[[.,[[.,.],.]],[.,.]],.]],[.,.]],.]],.]=>[.,[[.,[[.,.],[[.,[[.,.],[[.,[.,.]],.]]],.]]],.]]
[1,1,0,1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,0,0]=>[[.,[[.,[[[[.,[[.,.],.]],[.,.]],[.,.]],.]],.]],.]=>[.,[[.,[[.,[[.,.],[[.,.],[[.,[.,.]],.]]]],.]],.]]
[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]=>[[.,[[[.,[[.,[[[.,.],[.,.]],.]],.]],[.,.]],.]],.]=>[.,[[.,[[.,.],[[.,[[.,[[.,.],[.,.]]],.]],.]]],.]]
[1,1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0]=>[[.,[[.,[[[.,[[[.,.],[.,.]],.]],[.,.]],.]],.]],.]=>[.,[[.,[[.,[[.,.],[[.,[[.,.],[.,.]]],.]]],.]],.]]
[1,1,0,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[[.,[[.,[[.,[[[[.,.],[.,.]],[.,.]],.]],.]],.]],.]=>[.,[[.,[[.,[[.,[[.,.],[[.,.],[.,.]]]],.]],.]],.]]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[.,[.,.]],[[[[.,[.,[.,.]]],.],.],.]],.]=>[.,[[.,[.,[.,[[[.,.],.],.]]]],[[.,.],.]]]
[1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[.,[[[.,[[[.,.],[.,.]],.]],[.,.]],.]],.]=>[.,[[.,[[.,.],[[.,[[.,.],[.,.]]],.]]],.]]
[1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[[.,[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]],.]=>[.,[[.,[[[.,.],[[[.,[.,.]],.],.]],.]],.]]
[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[[.,[[.,[[[.,[[.,.],.]],[.,.]],.]],.]],.]=>[.,[[.,[[.,[[.,.],[[.,[.,.]],.]]],.]],.]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[.,[[.,.],.]],[.,[[[.,.],[.,.]],.]]],.]=>[.,[[[.,[[.,.],[.,.]]],.],[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[.,[[.,.],.]],[.,[[.,[[.,.],.]],.]]],.]=>[.,[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[[[[.,[[[.,.],[.,.]],.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,[[.,.],[.,.]]],.]]]]
[1,1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[[.,[[.,.],[[.,[.,.]],.]]],.],[.,.]],.]=>[.,[[.,.],[.,[[[.,[[.,.],.]],[.,.]],.]]]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0]=>[[[.,[[[.,[[.,.],.]],[.,.]],.]],[.,.]],.]=>[.,[[.,.],[[.,[[.,.],[[.,[.,.]],.]]],.]]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[.,[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]],[.,.]],.]=>[.,[[.,.],[[.,[[[[.,[[.,.],.]],[.,.]],.],.]],.]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[.,[[[.,.],[.,[[[.,.],[[.,.],.]],.]]],.]]=>[[.,[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]=>[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]],.]=>[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[.,[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]]=>[[[[[.,.],[.,.]],[[.,.],[.,.]]],.],.]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[[.,.],[[.,[[[[.,.],.],.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0]=>[[[[[[.,.],.],.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[[.,.],.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[[.,.],[.,[.,.]]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[[.,.],.],[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],[.,[.,.]]]]=>[[[[.,.],.],[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[[[.,[[.,[.,[.,.]]],.]],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[[.,[[[.,.],.],.]],.]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[[[.,.],[.,[.,.]]],[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],[[[.,.],.],[.,.]]]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[.,.],[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[[.,[.,[[[[.,.],.],.],[.,.]]]],[.,.]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,[[.,.],[[.,.],[.,.]]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[[.,.],[.,.]],[.,.]],.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]]=>[[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[[.,[[[.,.],[.,.]],.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,[[.,.],[.,.]]],.]]]
[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]=>[[[[.,[.,[[[.,[.,[.,.]]],.],.]]],.],.],.]=>[.,[.,[.,[[[.,[.,[[[.,.],.],.]]],.],.]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.],.]=>[.,[.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]]]
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[.,.],[[[[[.,[.,[.,[.,.]]]],.],.],.],.]]=>[[.,[.,[.,[.,[[[[.,.],.],.],.]]]]],[.,.]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,[.,.]],.],[[.,.],[[[.,[.,.]],.],.]]]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,[[.,.],.]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[[[[[.,[.,[.,[.,.]]]],[[.,.],.]],.],.],.]=>[.,[.,[.,[[.,[.,.]],[[[[.,.],.],.],.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[.,.],[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[[[[[.,[[.,.],[.,.]]],.],.],.],[.,.]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[.,[[.,[[[.,.],[[.,.],[[.,.],.]]],.]],.]]=>[[.,[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]],.]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[.,[.,.]],[.,[[.,.],[[.,.],[.,.]]]]]=>[[[[[.,.],[.,.]],[.,.]],.],[[.,.],.]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[[.,.],[.,[[[.,.],[.,.]],.]]],[.,.]],.]=>[.,[[.,.],[[[.,[[.,.],[.,.]]],.],[.,.]]]]
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]=>[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],.]],.]=>[.,[[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[[[[.,[.,[.,.]]],[[.,.],[[.,.],.]]],.],.]=>[.,[.,[[[.,[.,.]],[.,.]],[[[.,.],.],.]]]]
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[[[.,.],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]=>[.,[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],[.,.]]]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[[[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[.,.]],.],.]=>[.,[.,[[.,.],[[[[.,.],[.,.]],.],[[.,.],[.,.]]]]]]
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[[[.,.],[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.]=>[.,[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[[.,.],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]=>[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[.,.]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,.],.]],.]=>[.,[[.,[.,.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[.,[[.,.],.]]]],[[.,.],.]]=>[[.,[.,.]],[[[[.,[.,.]],.],[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[[.,[[[[[.,.],.],.],.],[.,.]]],[.,.]]
[1,1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[[[[.,[[.,[.,[.,[[.,.],.]]]],.]],.],.],.]=>[.,[.,[.,[[.,[[[[.,[.,.]],.],.],.]],.]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,1,0]=>[[[[[.,.],.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,[.,.]]]]]
[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]=>[[[[[.,.],.],[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[[.,.],[.,[[.,[[.,.],.]],[[.,.],.]]]],.]=>[.,[[[[.,[.,.]],[[.,[.,.]],.]],.],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[[.,[.,.]],[[.,[[.,.],.]],[[.,.],.]]],.]=>[.,[[[.,[.,.]],[[.,[.,.]],.]],[[.,.],.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]=>[.,[.,[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]=>[[[[[[[[.,.],.],.],[[.,.],.]],.],.],.],.]=>[.,[.,[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[[[.,.],.],[.,.]],.],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],.],[.,.]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],.]],.]=>[.,[[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],.]]
[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]=>[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.]=>[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,.],[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[[.,[[[[.,.],.],.],.]],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],.],[.,.]],[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[.,.],[[.,.],[[[[.,.],.],[[.,.],.]],.]]]=>[[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,.],[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],[.,.]]
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[[[[[[.,[.,[[[.,.],.],.]]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[.,[.,[[[[.,.],.],[.,.]],[[.,.],[.,.]]]]]=>[[[[[.,.],[.,.]],[[.,.],[.,[.,.]]]],.],.]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,.],[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[[.,.],[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],[.,.]],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[[.,.],[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],[.,.]],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]
[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]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.]=>[.,[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]]
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]],.]=>[.,[[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],[.,.]]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[.,[[.,.],[[.,.],[[[.,[.,.]],[.,.]],.]]]]=>[[[[.,[[.,.],[[.,.],.]]],[.,.]],[.,.]],.]
[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]=>[[.,[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]],.]=>[.,[[[.,.],[[.,.],[[.,[[.,.],.]],.]]],.]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0]=>[[[[.,[[.,[.,.]],.]],[.,.]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[.,.],[[.,[[.,.],.]],.]]]]
[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]=>[.,[[.,.],[[[[.,[.,.]],[.,.]],.],[[.,[.,.]],.]]]]=>[[[[.,[[.,.],.]],[.,[[.,.],[[.,.],.]]]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,.],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]]=>[[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],[.,.]],.]
[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]=>[.,[[[[.,[.,.]],[.,.]],.],[[[.,[.,.]],[.,.]],.]]]=>[[[.,[[.,.],[[.,.],.]]],[.,[[.,.],[[.,.],.]]]],.]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[.,[[[.,[[[.,[.,.]],[.,.]],.]],.],[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],[.,[[.,[[.,.],[[.,.],.]]],.]]],.]
[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]=>[[.,[[.,[.,.]],.]],[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]],.]=>[.,[[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]],.]=>[.,[[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]],.]=>[.,[[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]]
[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]=>[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]],.]=>[.,[[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.]]
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]],.]=>[.,[[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]]
[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]=>[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]],.]=>[.,[[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,1,0,0]=>[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[.,[[.,[[.,[[.,[[[.,.],.],.]],.]],.]],.]]=>[[.,[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[.,[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]]=>[[.,[[.,[[.,[[[.,.],.],.]],.]],.]],.]
          
Map
to binary tree: up step, left tree, down step, right tree
Description
Return the binary tree corresponding to the Dyck path under the transformation up step - left tree - down step - right tree.
A Dyck path $D$ of semilength $n$ with $ n > 1$ may be uniquely decomposed into $1L0R$ for Dyck paths L,R of respective semilengths $n_1, n_2$ with $n_1 + n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
Map
left-right symmetry
Description
Return the left-right symmetrized tree of a binary tree.