- FindStat

Identifier
Mp00029: Dyck paths —to binary tree: left tree, up step, right tree, down step⟶ 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]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]],.]=>[.,[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]],.]=>[.,[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]],.]=>[.,[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]],.]=>[.,[[[[[.,[[[.,.],.],.]],.],.],.],.]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]=>[.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]=>[.,[[[[[[[.,.],.],[.,.]],.],.],.],.]]
[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]=>[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[[[[[[[.,[[.,.],.]],.],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[[[[[[[.,.],.],[.,.]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]=>[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]],.]=>[.,[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]],.]=>[.,[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]],.]=>[.,[[[[[[.,[[[.,.],.],.]],.],.],.],.],.]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.]=>[.,[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]],.]=>[.,[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]],.]=>[.,[[[[.,[[[[.,.],.],.],.]],.],.],.]]
[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]=>[[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]],.]=>[.,[[[[[[.,.],[[.,.],.]],.],.],.],.]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]],.]=>[.,[[[[[[[.,.],.],.],[.,.]],.],.],.]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[[.,.],[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[[[[.,[[[[.,.],.],.],.]],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[[[[[[.,.],[[.,.],.]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[[[[[[.,[.,.]],[.,.]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[[[[[[[.,[.,[.,.]]],.],.],.],.],.],[.,.]]
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],[.,.]],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],[.,.]],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]=>[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]],.]=>[.,[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]],.]=>[.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]],.]=>[.,[[[.,[[[[[.,.],.],.],.],.]],.],.]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]],.]=>[.,[[[[[.,[.,[[.,.],.]]],.],.],.],.]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]],.]=>[.,[[[[[.,[[.,.],[.,.]]],.],.],.],.]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]],.]=>[.,[[[[[[[.,.],.],.],.],[.,.]],.],.]]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[[[[[.,[.,[[.,.],.]]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[[[[[.,[[.,.],[.,.]]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[[[[[[.,.],[.,[.,.]]],.],.],.],[.,.]]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],[.,.]],.],[.,.]]
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],[.,.]],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]],.]=>[.,[[[[.,[[[[[.,.],.],.],.],.]],.],.],.]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]],.]=>[.,[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.]=>[.,[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]=>[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]
[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]=>[[.,.],[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]=>[[[[.,[[[[[.,.],.],.],.],.]],.],.],[.,.]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]=>[[[[[[[.,.],[.,[.,.]]],.],.],.],.],[.,.]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]],.]=>[.,[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]],.]=>[.,[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]],.]=>[.,[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[[[.,.],.],.]],.]]]],.]=>[.,[[[[.,[[.,[.,[.,.]]],.]],.],.],.]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]],.]=>[.,[[[[.,[[[.,.],.],[.,.]]],.],.],.]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]],.]=>[.,[[[[[.,[.,.]],[[.,.],.]],.],.],.]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]=>[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[[.,.],[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],[.,.]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[[[[.,[[[.,.],.],[.,.]]],.],.],[.,.]]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[[[[[.,.],[[.,[.,.]],.]],.],.],[.,.]]
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]=>[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],[.,.]]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]=>[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[.,.],[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.]=>[.,[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[.,[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.]=>[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[[.,[[[[[[[.,.],.],.],.],.],.],.]],[.,.]]
[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]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]
[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]=>[[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.],.]=>[.,[.,[[[[[.,[[.,.],.]],.],.],.],.]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.],.]=>[.,[.,[[[[[[.,.],[.,.]],.],.],.],.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]],.]=>[.,[[[.,[[[[.,.],.],.],[.,.]]],.],.]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],[.,.]]=>[[.,.],[[[[[.,[.,[.,.]]],.],.],.],.]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[[.,.],[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[[[.,[[[.,[.,.]],[.,.]],.]],.],[.,.]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[[.,.],[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[[[.,[[[[.,.],.],.],[.,.]]],.],[.,.]]
[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[[.,.],[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[[[[[.,.],.],[[[.,.],.],.]],.],[.,.]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[]=>.=>.
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[[[.,.],.],.],.],.],[.,.]],.]]=>[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[[[[.,.],.],.],.],[.,.]],.],.]]=>[[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[[[.,.],.],.],.],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[[[[[.,.],.],.],.],[[.,.],.]],.]]=>[[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[[[[[.,.],.],.],.],[.,[.,.]]],.]]=>[[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]],.]
[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]=>[.,[[[[[[[.,.],.],.],[.,.]],.],.],.]]=>[[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[[[[[.,.],.],.],[[.,.],.]],.],.]]=>[[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[.,[[[[[.,.],.],.],[.,[.,[.,.]]]],.]]=>[[.,[[[[.,.],.],.],[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[.,.],.],[.,.]],.],.],.],.]]=>[[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],.],[[.,.],.]],.],.],.]]=>[[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]],.]
[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]=>[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[[.,.],[.,.]],[[.,.],[[.,.],.]]]]=>[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],.]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[[.,.],[.,.]],[[.,[[.,.],.]],.]]]=>[[[.,[[.,[.,.]],.]],[[.,.],[.,.]]],.]
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],[[.,.],[.,.]]],.]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],[[.,.],.]],.],.],.],.]]=>[[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]
[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]=>[.,[[[[[[.,.],[.,[.,.]]],.],.],.],.]]=>[[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]],.]
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[.,[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],[[[.,.],.],[.,.]]],.]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[[.,.],[.,[.,[.,.]]]],.],.],.]]=>[[.,[.,[.,[[[[.,.],.],.],[.,.]]]]],.]
[1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]]=>[[[[.,.],.],[[[[.,.],.],.],[.,.]]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[.,[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]]=>[[.,[.,[[[[[.,.],.],.],.],[.,.]]]],.]
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]]=>[[[[[[.,[.,[.,.]]],.],.],.],[.,.]],.]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]]=>[[[[[[[.,.],[.,.]],.],.],.],[.,.]],.]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]=>[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]]=>[[[.,[[[[[.,.],.],.],.],.]],[.,.]],.]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]]=>[[[[[[.,[[.,.],.]],.],.],.],[.,.]],.]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]=>[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[[.,[.,.]],.],.],.],.],[.,.]]]=>[[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]],.]
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],[.,[[.,.],.]]],.]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,[.,.]],[.,.]],.],.],.],.]]=>[[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],[[.,.],[[.,.],.]]],.]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],[[.,.],.]],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],[[.,[.,.]],.]],.]
[1,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[.,[[.,[[[[.,.],.],.],.]],[.,[.,.]]]]=>[[[[.,.],.],[[.,[.,[.,[.,.]]]],.]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]=>[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]
[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]=>[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]=>[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],[.,[.,.]]],.],.]
[1,1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[.,.],[[[.,.],.],.]],[.,.]]]]=>[[[[.,.],[[.,[.,[.,.]]],[.,.]]],.],.]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.]
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[.,[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]]=>[[[[[.,.],.],[[[.,.],.],[.,.]]],.],.]
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[[.,.],[.,[[[[.,.],.],.],.]]]]]=>[[[[[.,[.,[.,[.,.]]]],.],[.,.]],.],.]
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]]=>[[[[.,.],[[[[.,.],.],.],[.,.]]],.],.]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]]=>[[.,[[[[[[.,.],.],.],.],[.,.]],.]],.]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]=>[[[.,[[[[[.,.],.],.],.],[.,.]]],.],.]
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[.,[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]]=>[[[[.,[[[[.,.],.],.],.]],[.,.]],.],.]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[[.,[[.,.],.]],.]]],.]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]=>[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.]
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[[.,[.,.]],[[[[.,.],.],.],.]]]]=>[[[[.,[.,[.,[.,.]]]],[[.,.],.]],.],.]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[.,[[[.,.],.],.]]],[[.,.],.]]]=>[[[.,[.,.]],[[[.,[.,[.,.]]],.],.]],.]
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[.,[.,[[.,[[[.,.],.],.]],[.,[.,.]]]]]=>[[[[[.,.],.],[[.,[.,[.,.]]],.]],.],.]
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[[[[.,.],.],.],.]],[.,.]]]]=>[[[[.,.],[[.,[.,[.,[.,.]]]],.]],.],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[[[[.,.],.],.],.],.]],.]]]=>[[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[[[.,.],.],.],[[.,.],.]]]]]=>[[[[[.,[.,.]],[.,[.,[.,.]]]],.],.],.]
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[[.,.],.],[[[.,.],.],.]]]]]=>[[[[[.,[.,[.,.]]],[.,[.,.]]],.],.],.]
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],[.,[.,.]]],.],.],.]
[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]=>[.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]]=>[[[[[.,[.,[.,[.,.]]]],[.,.]],.],.],.]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]=>[[[[[[.,[.,.]],[.,.]],[.,.]],.],.],.]
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]]=>[[[[.,[.,[[[.,.],.],[.,.]]]],.],.],.]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]]=>[[[.,[[[[[.,.],.],.],[.,.]],.]],.],.]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]=>[[[[.,[[[[.,.],.],.],[.,.]]],.],.],.]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[.,[.,[.,.]]]],.],.],.],.]]=>[[.,[.,[.,[.,[[[[.,.],.],.],.]]]]],.]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]=>[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]=>[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[.,[[.,.],.]],.],.],.]]]]=>[[[[.,[.,[.,[[.,[.,.]],.]]]],.],.],.]
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[.,[[[.,.],.],.]],.],.]]]]=>[[[[.,[.,[[.,[.,[.,.]]],.]]],.],.],.]
[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]=>[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]=>[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]]=>[[[[[.,[[.,.],[.,[.,.]]]],.],.],.],.]
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]]=>[[[[[[[.,.],.],[.,[.,.]]],.],.],.],.]
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]]=>[[[[[[.,.],[[.,.],[.,.]]],.],.],.],.]
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]]=>[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]]=>[[[.,[[[[[.,.],.],[.,.]],.],.]],.],.]
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]]=>[[[[.,[[[[.,.],.],[.,.]],.]],.],.],.]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]=>[[[[[.,[[[.,.],.],[.,.]]],.],.],.],.]
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]]=>[[[[[[.,[[.,.],.]],[.,.]],.],.],.],.]
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]]=>[[[[[[[.,[.,.]],.],[.,.]],.],.],.],.]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]]=>[[.,[.,[.,[[[[[.,.],.],.],.],.]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]]=>[[[.,.],[.,[[[[[.,.],.],.],.],.]]],.]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]]=>[[.,[[.,.],[[[[[.,.],.],.],.],.]]],.]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]]=>[[[.,[.,.]],[[[[[.,.],.],.],.],.]],.]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]]=>[[[[.,.],.],[[[[[.,.],.],.],.],.]],.]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]=>[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]]=>[[[[.,[[.,[[.,[.,.]],.]],.]],.],.],.]
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]]=>[[[[[.,[.,[[.,[.,.]],.]]],.],.],.],.]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]]=>[[.,[[[[[.,[.,[.,.]]],.],.],.],.]],.]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]]=>[[[[[.,[[.,[.,[.,.]]],.]],.],.],.],.]
[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]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]]=>[[[[.,.],[[[[[.,.],.],.],.],.]],.],.]
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]]=>[[[[[.,.],[[[[.,.],.],.],.]],.],.],.]
[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]=>[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]=>[[[[[[.,.],[[[.,.],.],.]],.],.],.],.]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]]=>[[[[[.,[[.,[[.,.],.]],.]],.],.],.],.]
[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]=>[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]=>[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.]
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]]=>[[[[[.,[[[.,[.,.]],.],.]],.],.],.],.]
[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]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[[[[.,.],.],.],.],.],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]
[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]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[[.,.],.]]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[[[[[.,.],.],.],.],.],.],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[[[[.,.],.],.],.],[.,[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]],.]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[[[.,.],.],.],[.,[[[[.,.],.],.],.]]]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[[[.,.],.],.],[.,[[[.,.],.],[.,.]]]]=>[[[[.,.],[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,.],.],[[.,[[.,.],[[.,.],.]]],.]]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[.,.],.],[.,[[[[[.,.],.],.],.],.]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[.,.],[[.,[[[[[.,.],.],.],.],.]],.]]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],[.,.]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[.,.],.],[.,[[[[.,.],.],.],[.,.]]]]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,[.,.]]]
[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]=>[[.,.],[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[[.,[[[.,[[.,.],.]],[.,.]],.]],[.,.]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[[.,.],[.,[[.,.],[[[[.,.],.],.],.]]]]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],[.,.]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[[[.,.],.],.],.],.]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,[.,[[.,.],.]]]]]=>[[[[[.,[.,.]],.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[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]=>[[.,.],[.,[[[[[[[.,.],.],.],.],.],.],.]]]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],[.,.]]
[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[[[.,.],.],.]]]]]=>[[[[[.,[.,[.,.]]],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[[[[.,.],.],.],.],.],.]]]]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[[[[[[.,.],.],.],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[[[.,.],.],.],.],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[[[[[[.,.],.],.],.],[.,[.,.]]],.],.]=>[.,[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[[[.,.],.],.],.],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[[.,.],.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[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]=>[[[[[.,.],.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[[.,.],.],[.,.]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[[[.,.],.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],.],[.,[.,.]]],.],.],.],.]=>[.,[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,[.,.]]]=>[[[.,.],.],[[[[.,.],.],.],[.,[.,.]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[[[.,.],.],[.,[.,[.,[.,.]]]]],.],.]=>[.,[.,[[[[[.,.],.],.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],[.,.]]=>[[.,.],[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[.,.],[.,.]],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[[.,.],[.,.]],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[[.,.],[.,.]],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.]=>[.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[.,.],[.,.]]]]
[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]=>[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[.,[.,[.,.]]]],.],.],.],.]=>[.,[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[[[[[.,.],[.,[.,[.,.]]]],[.,.]],.],.]=>[.,[.,[[.,.],[[[[.,.],.],.],[.,.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[.,.],.],.],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.]=>[.,[.,[.,[[[[[.,.],.],.],.],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[[[.,.],.],[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]=>[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[[.,[.,.]],.],.],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[[.,[.,.]],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[[.,[.,.]],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[[.,[.,.]],.],.],[.,.]],.],.],.]=>[.,[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[[.,[.,.]],.],.],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[[.,[.,.]],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[.,.]],.],[.,.]],.],.],.],.]=>[.,[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]]
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[.,[.,.]],[.,.]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[.,[.,.]],[.,.]],[.,.]],.],.],.]=>[.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[[.,[.,.]],[.,[.,[.,.]]]],.],.],.]=>[.,[.,[.,[[[[.,.],.],.],[[.,.],.]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[.,[.,[.,.]]],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[.,[.,[.,.]]],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,[.,[.,.]]],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.]=>[.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,.]]],[.,[.,.]]],.],.],.]=>[.,[.,[.,[[[.,.],.],[[[.,.],.],.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[[[.,.],.],.],.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[[[.,.],.],.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,[.,.]]]],[.,.]],.],.],.]=>[.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[[[.,.],.],.],.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.],.]=>[.,[.,[[[.,.],.],[[[[.,.],.],.],.]]]]
[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]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],[.,.]]=>[[.,.],[.,[.,[[[[[.,.],.],.],.],.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]],.]=>[.,[[.,.],[.,[[[[[.,.],.],.],.],.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.]=>[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[[[[.,.],.],.],.],.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]]=>[[.,.],[.,[[[[[[.,.],.],.],.],.],.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]=>[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[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]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[[[.,.],.],.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[.,.],.],.],[.,.]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[[.,.],.],[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[.,.],.],.],[.,[.,.]]]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],[.,.]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[.,.],[.,[.,.]]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[[.,.],.],[.,.]]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,[.,.]],.],[.,.]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]]]
[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]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[[[.,.],.],[[.,.],.]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[[[.,.],.],.],[[.,.],.]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[.,[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[.,[.,[.,.]]],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,[.,[.,.]]],[.,.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,.],[[[.,.],.],.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[.,.],.],[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[[[.,.],.],.],.]]]]
[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]=>[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]],.]=>[.,[[.,.],[.,[[[[[[.,.],.],.],.],.],.]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],[.,.]]=>[[.,.],[.,[[[[[[[.,.],.],.],.],.],.],.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.]=>[.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[[[.,.],.],.]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]
[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]=>[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[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]=>[.,[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]]=>[[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[[[.,[.,.]],.],.],.],.],.],[[.,.],.]]=>[[.,[.,.]],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[.,[[.,.],.]],.],.],.],[[.,.],.]]=>[[.,[.,.]],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[[.,.],[.,.]],.],.],.],[[.,.],.]]=>[[.,[.,.]],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[[[[.,.],.],.],.],.],.]]],.]=>[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[[[[.,.],.],.],.],.]]],.],.]=>[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[[[[.,.],.],.],.]]],.],.],.]=>[.,[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[[[.,.],.],.]]],.],.],.],.]=>[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[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]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]=>[[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]],.]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.]=>[.,[.,[[.,[[[[[.,.],.],.],.],.]],.]]]
[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]=>[[.,[[.,.],[[[[[.,.],.],.],.],.]]],.]=>[.,[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]=>[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]
[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]=>[[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[.,[.,.]],.],.]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[.,[.,.]],.],.],.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]]=>[[[.,.],.],[[[[[.,[.,.]],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[[[.,.],.],.]],.],.],.],.]=>[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],.],[[.,.],.]],.],.],.],.]=>[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.]=>[.,[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[[[[.,.],.],.],.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[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]=>[[.,.],[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]=>[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]
[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]=>[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]]=>[[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[[[[.,.],.],.],.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]=>[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]
[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]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],[.,.]]=>[[.,.],[[.,[[[[[.,.],.],.],.],.]],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[[[[[.,.],.],.],.],[[[.,.],.],.]],.]=>[.,[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[[[[[[.,.],.],.],.],[[.,.],.]],.],.]=>[.,[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],[[.,.],.]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],[[[.,.],.],.]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[[[[[.,.],.],.],.],[[.,.],.]],[.,.]]=>[[.,.],[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]]=>[[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[[.,.],.]],[.,.]],.],.],.],.]=>[.,[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[[.,.],[.,.]],.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,[[.,.],[.,.]]],.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[[.,.],[.,.]],[.,.]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[.,.],[[.,.],[.,.]]],.]]]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[[[.,.],[.,.]],[[.,[.,.]],.]]],.]=>[.,[[[.,[[.,.],.]],[[.,.],[.,.]]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]]=>[[.,.],[[[.,.],[[.,.],[[.,.],[.,.]]]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.]
[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]=>[.,[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]=>[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]]=>[[[[[[[.,.],[[[.,.],.],.]],.],.],.],.],.]
[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]=>[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]=>[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]=>[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]=>[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]=>[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]=>[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]]=>[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],[.,.]]
[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]=>[[.,.],[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]]=>[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],[.,.]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],[[.,.],.]]=>[[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]
[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]=>[[.,[.,[.,[[[[[.,.],.],.],.],.]]]],.]=>[.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]],.]=>[.,[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[[[[.,.],.],.],.],[.,.]]]],.]=>[.,[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]],.]=>[.,[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]]
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]]=>[[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.],.]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]],.]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[.,[[.,.],.]],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[.,[[.,.],.]],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[[.,.],.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[[[.,.],.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[[[[.,.],.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[[[[.,.],.],.],.],.],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[[[[.,.],.],.],.],.]]=>[[.,[.,[.,[.,[.,.]]]]],[[[.,.],.],.]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,.]]]],[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],[[[[.,.],.],.],.]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,[.,[[.,.],.]]]],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[[[[.,[.,.]],.],.],.]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,[.,[[[.,.],.],.]]]],[[.,.],.]]=>[[.,[.,.]],[[[[.,[.,[.,.]]],.],.],.]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],[.,.]]=>[[.,.],[[[[.,[.,[.,[.,.]]]],.],.],.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]=>[[.,.],[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[[[.,.],.],[[[.,.],.],.]]],.],.]=>[.,[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]=>[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]]=>[[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.],.]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],[.,.]]]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]]=>[[[[[[[.,[[.,[.,.]],.]],.],.],.],.],.],.]
[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[[[[[[.,[.,.]],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.]=>[.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,[.,[.,[[.,.],.]]]]],[[.,.],.]]=>[[.,[.,.]],[[[[[.,[.,.]],.],.],.],.]]
[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],[[.,.],.]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[.,.],[[[[[[.,.],.],.],[.,.]],.],.]]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],[.,.]]
[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]=>[[.,[.,.]],[[[[[[[.,.],.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[[.,.],.]],[[[[[.,.],.],.],.],.]]=>[[.,[.,[.,[.,[.,.]]]]],[[.,[.,.]],.]]
[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]=>[.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]]=>[[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[[[.,.],.],.],.],.],[[.,.],.]],.]=>[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.]=>[.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[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]=>[[[.,.],[[[[[.,.],.],.],.],.]],[.,.]]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[[.,.],[[[[[[.,.],.],.],.],.],.]],.],.]=>[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]=>[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[[.,.],[[[[[.,.],.],.],[.,.]],[.,.]]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[[.,.],[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]=>[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],.]=>[.,[[[.,.],[.,.]],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[[[.,.],.],.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,[.,[.,.]]],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[[[.,.],.],.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,[.,[.,.]]],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[[[[[[.,[.,.]],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[[.,.],.],[[.,.],[.,[.,[[.,.],.]]]]]=>[[[[[.,[.,.]],.],.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[[[.,.],.],[[.,.],[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[[[[.,.],.],.],.],[.,.]],.]],.]=>[.,[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[[[[[.,.],.],.],.],[[.,.],.]]],.]=>[.,[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[[[.,.],.],.],.]],[[.,.],.]],.]=>[.,[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[.,[[[[.,.],.],.],.]],.],.],.]],.]=>[.,[[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]],.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[[.,.],.],[[.,.],.]],.],.],.]],.]=>[.,[[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]],.]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[[[[.,.],.],.],.],.]]=>[[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[[.,[.,.]],.],.],.],[[.,.],.]],.]=>[.,[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[[[.,.],.],.],.],[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[[[.,.],.],.],.],.]]]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[[[[[.,.],.],.],.],.],.]]],.],.]=>[.,[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[[[[[.,.],.],.],.],.]]],.],.],.]=>[.,[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[[[[.,.],.],.],.]]],.],.],.],.]=>[.,[.,[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,[[[.,.],.],.]]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[[[[[.,.],.],.],.],.],.],.]],[.,.]]=>[[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[[[[[.,.],.],.],.],.]],[[.,.],.]]=>[[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.],.]=>[.,[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]]
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[[[[[.,[.,.]],.],.],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],.]],.]=>[.,[[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,[[.,[.,.]],.]],.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],[[.,.],.]],.]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[.,[.,[.,.]]],[[.,[.,[.,[.,.]]]],.]]=>[[.,[[[[.,.],.],.],.]],[[[.,.],.],.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.],.]=>[.,[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[[[[.,.],.],.],.]],.]]],.]=>[.,[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[[[[[.,.],.],.],.],[[.,.],[.,.]]],.]=>[.,[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]=>[.,[.,[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],.],[[.,.],.]],.],.],.],.]=>[.,[.,[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[[.,[.,.]],.],.],.],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[.,[.,[.,[[.,.],.]]]]]
[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]=>[[[[[[.,.],[[.,.],[.,.]]],.],.],.],.]=>[.,[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[[.,[.,.]],.],.],.],.]]
[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]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[[[[.,.],.],.],.]],.],.],.],.]=>[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[[[.,.],.],.]],[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],[[.,[.,[.,.]]],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[[[[.,.],.],.],[.,.]]]],.],.]=>[.,[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[[[[[.,[.,.]],.],[[.,.],.]],.],.],.]=>[.,[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0]=>[[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]],.]=>[.,[[[[.,.],.],[[[[.,.],.],.],.]],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[[[.,.],.],.],.],[[.,.],.]]]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],.]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[[[.,.],[[[[[.,.],.],.],.],.]],[.,.]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[.,[.,[.,.]]],[.,[[.,[.,[.,.]]],.]]]=>[[[.,[[[.,.],.],.]],.],[[[.,.],.],.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,[[.,.],[.,.]]],.]],[.,.]],.]=>[.,[[.,.],[[.,[[[.,.],[.,.]],.]],.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]=>[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.]=>[.,[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[[.,.],[[.,.],.]],.]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[[.,[.,.]],[.,.]]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[[.,.],[[.,.],.]],.]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[[[.,[[.,.],[[.,[[.,.],.]],.]]],.],.]=>[.,[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],[[[[[.,.],.],.],.],[.,.]]],.]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,[[[.,.],.],.]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[[.,.],.],[[[[[.,.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[.,[[[.,.],.],.]],.],.],[[.,.],.]]=>[[.,[.,.]],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[[[.,.],.],.],.],.]],.]],.]=>[.,[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.],.]=>[.,[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]]
[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]=>[[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]],.]=>[.,[[[.,.],[[[[[.,.],.],.],.],.]],.]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[[.,.],[.,[[.,[[[[.,.],.],.],.]],.]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],[.,.]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,[.,.]]]=>[[[.,.],.],[[[[[.,.],.],[.,.]],.],.]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]]=>[[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[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]=>[[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],[[.,.],.]],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],[.,.]]]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[[[.,.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]]=>[[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]]=>[[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]],.]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[[.,.],[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[.,.],[[.,.],.]]]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,[[.,.],[.,.]]],[.,.]],.]]=>[[.,[[.,.],[[[.,.],[.,.]],.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[[.,.],[.,.]]],[[[.,.],[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[[.,.],[.,.]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[.,[.,[.,.]]],.],.],.],[[.,.],.]]=>[[.,[.,.]],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,[[.,.],.]],.],[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[[[[[.,.],.],.],.],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[[.,.],[[[[[.,.],.],.],.],.]],.],.]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]]
[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]=>[[.,[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.],.]=>[.,[.,[[[.,.],[[.,.],[[.,.],[.,.]]]],.]]]
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]]]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.],.]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,.],[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[[.,[[[[[.,.],.],.],.],[.,.]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]],.]=>[.,[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[[[[.,.],.],.],.],[[[.,.],.],[.,.]]]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],[.,.]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[[.,.],[.,.]],[[[.,[.,.]],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[[.,.],.]]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,[.,.]],[.,.]]]=>[[[.,.],[[.,.],.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[[.,.],[.,.]]]],.],.],.],.]=>[.,[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[[[.,.],.],[.,.]]]],.],.],.]=>[.,[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[[[.,[.,.]],.],.],.]]],.],.]=>[.,[.,[[[.,[.,[.,[[.,.],.]]]],.],.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]=>[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]=>[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]=>[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],[.,.]]=>[[.,.],[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],[.,.]]=>[[.,.],[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>[[.,.],[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],[.,.]]=>[[.,.],[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>[[.,.],[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>[[.,.],[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],[.,.]]=>[[.,.],[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],[.,.]]=>[[.,.],[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]=>[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]]=>[[.,.],[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],.]]=>[[.,[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]],.]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],.]]=>[[.,[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],.]]=>[[.,[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]],.]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],.]]=>[[.,[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]]=>[[.,[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]],.]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],[[.,.],.]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>[[.,[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]],.]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]]=>[[.,[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]]=>[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]],.]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],[[.,.],.]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[[[.,[.,.]],[.,.]],.]]=>[[.,[[.,.],[[.,.],.]]],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],[[.,.],.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>[[.,[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]]=>[[.,[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,[[.,.],.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]]=>[[.,[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],[[.,.],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]],.]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,[[[.,.],.],.]],[.,[[.,.],.]]],.]=>[.,[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]],.]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[[[.,.],[.,.]],.]]],[.,.]],.]=>[.,[[.,.],[[[.,[[.,.],[.,.]]],.],.]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]]]=>[[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.],.]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],[.,.]]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]]=>[[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]],.]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[[.,.],[[.,.],.]],.]],[.,.]],.]=>[.,[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],[[.,[.,.]],.]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]],.]=>[.,[[.,.],[[[[[.,[.,.]],.],.],.],.]]]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[.,[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[[.,[[.,.],.]],.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[[.,[[.,.],.]],.],.]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]],.]=>[.,[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]],.]=>[.,[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[[.,.],[[.,.],[[.,.],.]]]]],.]=>[.,[[[[[.,[.,.]],[.,.]],[.,.]],.],[.,.]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,[[.,.],[[.,.],.]]]],.]],.]=>[.,[[.,[[[[.,[.,.]],[.,.]],.],.]],[.,.]]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,[.,[[.,.],.]]],.]],.]],.]=>[.,[[.,[[.,[[[.,[.,.]],.],.]],.]],[.,.]]]
[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]=>[[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]=>[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[[[.,.],[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]],.]=>[.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.],[.,.]]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[[[[.,.],[.,.]],.],[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[[[.,.],[.,[[[.,.],[.,.]],.]]],[.,[[.,.],[.,.]]]]
[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]=>[[[.,.],[[.,[[.,[.,[[[.,.],[.,.]],.]]],.]],.]],.]=>[.,[[.,[[.,[[[.,[[.,.],[.,.]]],.],.]],.]],[.,.]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[[.,.],[.,.]],.],[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[[.,.],[[.,[.,.]],.]],.]]]]=>[[[[.,[[.,[[.,.],.]],[.,.]]],[.,.]],[.,.]],[.,.]]
[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]=>[[[.,.],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]=>[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]=>[[.,[.,.]],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],[[[[[.,.],.],.],.],.]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,.]]]],[[[[[.,.],.],.],.],.]]=>[[.,[.,[.,[.,[.,.]]]]],[[[[.,.],.],.],.]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[[[[[.,.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[[.,.],.],.]]
[1,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]]]=>[[[[[[[.,.],[.,[.,[.,.]]]],.],.],.],.],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[[[.,.],[.,.]],.],.],.],.],[[.,.],.]]=>[[.,[.,.]],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[[.,.],[.,.]],.],.],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[[[[.,.],.],.],.],.],[[.,.],.]]]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[[[.,.],[.,.]],.]],[.,.]]],.]=>[.,[[[.,.],[[.,[[.,.],[.,.]]],.]],.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[.,.],[.,.]],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]]=>[[.,.],[[[.,.],[.,.]],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,[[.,[.,.]],.]],[[.,.],[.,.]]],.]=>[.,[[[.,.],[.,.]],[[.,[[.,.],.]],.]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,[.,.]]]=>[[[.,.],.],[[[[[.,.],.],.],[.,.]],.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,[[.,.],[.,.]]],.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,[[[.,.],[.,.]],.]],.]]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]]=>[[.,[[[.,.],[[.,.],[[.,.],[.,.]]]],.]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[[.,.],[.,.]],[[.,.],[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[.,.]]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],[[.,.],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],[.,.]]]=>[[[.,.],[[.,.],.]],[[.,[[.,.],.]],.]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[.,.],[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]=>[[[[[[.,.],[.,.]],[.,.]],[.,.]],.],[.,.]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,[[.,[.,.]],.]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[.,[[.,.],.]],.],.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,.],[[.,[.,.]],.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,[[.,.],.]],[.,.]]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,[[.,.],[.,.]]],.]],.]],.]=>[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],[.,.]]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,.],[[.,.],[[.,[.,.]],.]]]],.],.]=>[.,[.,[[[[.,[[.,.],.]],[.,.]],[.,.]],.]]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,[[.,[.,.]],.]],.]]],.]=>[.,[[[.,[[.,[[.,.],.]],.]],[.,.]],[.,.]]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[[[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],.],.]=>[.,[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,.],[[.,.],[.,.]]]],.]],.]=>[.,[[.,[[[[.,.],[.,.]],[.,.]],.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]],.]=>[.,[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]=>[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]],.]]=>[[.,[[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]],.]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]=>[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],.]]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[.,[[[.,[.,.]],.],[[.,.],[[.,[.,.]],.]]]]=>[[[[.,[[.,.],.]],[.,.]],[.,[[.,.],.]]],.]
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],[.,[[.,[[.,.],.]],.]]],.]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],[.,[[[.,.],[.,.]],.]]],.]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]]=>[[[.,.],[.,[[.,[[[.,.],[.,.]],.]],.]]],.]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[.,[[[.,[[.,[.,.]],.]],.],[[.,.],[[.,[.,.]],.]]]]=>[[[[.,[[.,.],.]],[.,.]],[.,[[.,[[.,.],.]],.]]],.]
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],[[.,[[.,.],[.,.]]],.]]]=>[[[.,[[[.,.],[.,.]],.]],[.,[[[.,.],[.,.]],.]]],.]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],[.,[[.,[[[.,.],[.,.]],.]],.]]],.]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,[[.,.],[[.,[.,.]],.]]],.],[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],[.,[[[.,[[.,.],.]],[.,.]],.]]],.]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[.,.],[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]]=>[[[[.,.],[[.,.],.]],[.,[[.,.],.]]],[.,.]]
[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]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]]=>[[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]]=>[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[.,.],[[[.,.],[.,.]],.]],[.,.]],.]=>[.,[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[[.,.],[[.,[.,.]],.]]],[.,.]],.]=>[.,[[.,.],[[[.,[[.,.],.]],[.,.]],[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[[[.,.],.],[[.,.],.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[[.,[.,.]],.],.]],.]],.]],.]=>[.,[[.,[[.,[[.,[.,[[.,.],.]]],.]],.]],.]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[.,[[[.,[.,.]],.],.]],.]],.]],.]],.]=>[.,[[.,[[.,[[.,[[.,[.,[[.,.],.]]],.]],.]],.]],.]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,.]],[[[.,.],.],.]],.],.],.],.]=>[.,[.,[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],[.,.]],[[.,.],.]],.],.],.],.]=>[.,[.,[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[[.,.],[.,.]],[.,.]],.]],.]],.]=>[.,[[.,[[.,[[.,.],[[.,.],[.,.]]]],.]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[[[.,.],.],.]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]=>[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]],.]=>[.,[[.,[[[[[.,.],.],.],.],[.,.]]],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]],.]=>[.,[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,[[.,.],.]]],[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],[[[.,[.,.]],.],.]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[[.,.],[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]]=>[[[[.,.],[[.,.],[[.,.],.]]],[.,.]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],.],[[.,[.,.]],.]]],.]]=>[[.,[[[.,[[.,.],.]],[.,[[.,.],.]]],.]],.]
[1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],.],[[.,.],[[.,[.,.]],.]]]],.]]=>[[.,[[[[.,[[.,.],.]],[.,.]],[.,[[.,.],.]]],.]],.]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[[.,[.,[.,.]]],.]],.],.]],.]=>[.,[[.,[.,[[.,[[[.,.],.],.]],.]]],.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[[.,[.,[.,.]]],.]],.]],.],.]=>[.,[.,[[.,[[.,[[[.,.],.],.]],.]],.]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[[.,[.,[.,.]]],.]]],.],.],.]=>[.,[.,[.,[[[.,[[[.,.],.],.]],.],.]]]]
[1,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,[.,.]],[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],[[.,.],.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]],.]=>[.,[[.,[[[.,[[.,[[.,.],.]],.]],.],.]],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,[[.,[[.,.],.]],.]]],.]],[.,.]]=>[[.,.],[[.,[[[.,[[.,[.,.]],.]],.],.]],.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,[[.,[[.,[.,.]],.]],.]],.],.]],.]],.]=>[.,[[.,[[.,[.,[[.,[[.,[[.,.],.]],.]],.]]],.]],.]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[.,.],.],[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],[.,[[.,[[.,.],.]],.]]],[.,[.,.]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],[.,[.,[.,.]]]],.]],[.,.]]=>[[.,.],[[.,[[[[.,.],.],.],[.,.]]],.]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[.,[[[[.,[.,.]],.],[[.,.],[.,.]]],[.,.]]]=>[[[.,.],[[[.,.],[.,.]],[.,[[.,.],.]]]],.]
[1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]
[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]=>[[[.,[[.,[.,[[.,.],.]]],.]],[.,.]],.]=>[.,[[.,.],[[.,[[[.,[.,.]],.],.]],.]]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]=>[[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]],.]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,[.,[.,.]]],.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,[[[.,.],.],.]],.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[[[[.,.],.],.],.],.],[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,[.,[[.,.],.]]],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[[[.,[.,.]],.],.]]]
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],[.,[.,.]]],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]],.]=>[.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.]=>[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[[[.,.],.],[.,[[.,[.,.]],.]]],[.,.]],.]=>[.,[[.,.],[[[.,[[.,.],.]],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[[.,.],.],[.,[[.,[.,.]],.]]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[[.,[[.,.],.]],.],[.,[.,.]]]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[[.,.],[[.,.],.]]],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[[[.,[.,.]],[.,.]],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[[.,[[.,[.,.]],.]],.]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[[.,.],[[.,.],[[.,.],.]]]],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[[.,.],[[.,[[.,.],.]],.]]],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[[[.,[[.,[.,.]],.]],[.,.]],.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[[.,[[.,.],.]],[[.,.],.]]],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[[[.,[.,.]],[[.,[.,.]],.]],.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[[.,[[.,.],[[.,.],.]]],.]],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[[.,[[[.,[.,.]],[.,.]],.]],.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]=>[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]]=>[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]]=>[[.,[[.,[[[.,.],[[.,.],[.,.]]],.]],.]],.]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[[.,.],[.,.]],.]],[.,.]],.],.]=>[.,[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.]=>[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,[.,.]]]=>[[[.,.],.],[[[[.,.],.],[[.,.],.]],.]]
[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]=>[[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[.,[[.,.],.]]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,[[.,.],.]],.]]=>[[.,[[.,[.,.]],.]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],[[.,.],.]]=>[[.,[.,.]],[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,.],[.,.]],[[.,[[.,.],[[.,.],.]]],.]]=>[[.,[[[.,[.,.]],[.,.]],.]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[.,[[.,[[.,.],.]],.]],.]]=>[[.,[[.,[[.,[.,.]],.]],.]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,.],[.,[[.,.],.]]],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[[[.,[.,.]],.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,.],[.,[[.,.],.]]],[[.,[[.,.],.]],.]]=>[[.,[[.,[.,.]],.]],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[[.,.],[[.,.],.]]]],[[.,.],.]]=>[[.,[.,.]],[[[[.,[.,.]],[.,.]],.],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[[.,[[.,.],.]],.]]],[[.,.],.]]=>[[.,[.,.]],[[[.,[[.,[.,.]],.]],.],[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,[[.,.],.]],[.,.]],[[.,[[.,.],.]],.]]=>[[.,[[.,[.,.]],.]],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],[[.,.],.]]=>[[.,[.,.]],[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[[.,[[.,.],.]],.]]],.]]=>[[.,[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,.],[[.,[[.,.],.]],[[.,.],.]]],.]]=>[[.,[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]],.]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[[.,.],[[.,.],.]]],.]],.]]=>[[.,[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[[.,.],[[.,.],.]]],.]]=>[[.,[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]],.]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[[.,[[.,.],.]],.]],.]]=>[[.,[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]],.]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[[.,.],[[.,.],.]]],[[.,.],.]],.]]=>[[.,[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]],.]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[[.,[[.,.],.]],.]],[[.,.],.]],.]]=>[[.,[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]],.]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],[[.,.],[[.,.],.]]]],.],.]]=>[[.,[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]],.]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],[[.,[[.,.],.]],.]]],.],.]]=>[[.,[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]],.]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[[.,.],.]],[[.,.],.]]],.],.]]=>[[.,[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]],.]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[[.,.],[[.,.],.]]],.]],.],.]]=>[[.,[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]],.]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[[.,[[.,.],.]],.]],.]],.],.]]=>[[.,[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,[[.,.],.]],.]]=>[[.,[[.,[.,.]],.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[[[.,.],[.,.]],[.,.]],[.,[[.,.],.]]],[[.,.],.]]=>[[.,[.,.]],[[[.,[.,.]],.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,[[.,.],[[.,.],.]]],.]]=>[[.,[[[.,[.,.]],[.,.]],.]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,[[.,[[.,.],.]],.]],.]]=>[[.,[[.,[[.,[.,.]],.]],.]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[[.,.],[.,.]],[.,[[.,.],.]]],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[[[.,[.,.]],.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],[[.,[[.,.],.]],.]]=>[[.,[[.,[.,.]],.]],[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[[.,.],[.,.]],[.,[[.,.],[[.,.],.]]]],[[.,.],.]]=>[[.,[.,.]],[[[[.,[.,.]],[.,.]],.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[[[.,.],[.,.]],[.,[[.,[[.,.],.]],.]]],[[.,.],.]]=>[[.,[.,.]],[[[.,[[.,[.,.]],.]],.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[.,.],[.,.]],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[.,.],[.,.]],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]=>[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,.],[.,.]],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]=>[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]=>[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]=>[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[[.,.],[.,[[.,.],.]]],[.,.]],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[[.,.],[[[.,[.,.]],.],[.,.]]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[[.,.],[.,[[.,.],.]]],[.,.]],[[.,[[.,.],.]],.]]=>[[.,[[.,[.,.]],.]],[[.,.],[[[.,[.,.]],.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[[.,.],[.,[[.,.],.]]],[.,[[.,.],.]]],[[.,.],.]]=>[[.,[.,.]],[[[.,[.,.]],.],[[[.,[.,.]],.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,.],[.,[[.,.],.]]],[[.,[[.,.],[[.,.],.]]],.]]=>[[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[.,.],[.,[[.,.],.]]],[[.,[[.,[[.,.],.]],.]],.]]=>[[.,[[.,[[.,[.,.]],.]],.]],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,.],[.,[[.,.],[[.,.],.]]]],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[[[[.,[.,.]],[.,.]],.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,.],[.,[[.,.],[[.,.],.]]]],[[.,[[.,.],.]],.]]=>[[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],.],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,.],[.,[[.,[[.,.],.]],.]]],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[[[.,[[.,[.,.]],.]],.],[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,.],[.,[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],.]]=>[[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],.],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[[.,.],[[.,.],[[.,.],.]]]]],[[.,.],.]]=>[[.,[.,.]],[[[[[.,[.,.]],[.,.]],[.,.]],.],[.,.]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[[.,.],[[.,[[.,.],.]],.]]]],[[.,.],.]]=>[[.,[.,.]],[[[[.,[[.,[.,.]],.]],[.,.]],.],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[[.,[[.,.],.]],[[.,.],.]]]],[[.,.],.]]=>[[.,[.,.]],[[[[.,[.,.]],[[.,[.,.]],.]],.],[.,.]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[[.,[[.,.],[[.,.],.]]],.]]],[[.,.],.]]=>[[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],.],[.,.]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[[.,[[.,[[.,.],.]],.]],.]]],[[.,.],.]]=>[[.,[.,.]],[[[.,[[.,[[.,[.,.]],.]],.]],.],[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,[[.,.],.]],[.,.]],[[.,[[.,.],[[.,.],.]]],.]]=>[[.,[[[.,[.,.]],[.,.]],.]],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[.,[[.,.],.]],[.,.]],[[.,[[.,[[.,.],.]],.]],.]]=>[[.,[[.,[[.,[.,.]],.]],.]],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],[[.,[[.,.],.]],.]]=>[[.,[[.,[.,.]],.]],[[[.,[.,.]],.],[[.,[.,.]],.]]]
[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]=>[[[.,[[.,.],.]],[.,[[.,[[.,.],.]],.]]],[[.,.],.]]=>[[.,[.,.]],[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,[[.,.],[[.,.],.]]],[.,.]],[[.,[[.,.],.]],.]]=>[[.,[[.,[.,.]],.]],[[.,.],[[[.,[.,.]],[.,.]],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,[[.,.],[[.,.],.]]],[.,[[.,.],.]]],[[.,.],.]]=>[[.,[.,.]],[[[.,[.,.]],.],[[[.,[.,.]],[.,.]],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],[[.,[[.,.],.]],.]]=>[[.,[[.,[.,.]],.]],[[.,.],[[.,[[.,[.,.]],.]],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,[[.,[[.,.],.]],.]],[.,[[.,.],.]]],[[.,.],.]]=>[[.,[.,.]],[[[.,[.,.]],.],[[.,[[.,[.,.]],.]],.]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]]=>[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]]=>[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]]=>[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]]=>[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]]=>[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.]]=>[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.]]=>[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]],.]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]]=>[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]],.]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]]=>[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]]],.]
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]]=>[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]],.]
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]]=>[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]],.]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]]=>[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]]],.]
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]]=>[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]],.]]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]],.]
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]],.]]=>[[.,[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]],.]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]],.]]=>[[.,[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]]],.]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]],.]]=>[[.,[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]],.]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]],.]]=>[[.,[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]],.]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]],.]]=>[[.,[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]]],.]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]],.]]=>[[.,[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]],.]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]],.]]=>[[.,[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]]],.]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]],.]]=>[[.,[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]],.]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]],.]]=>[[.,[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]],.]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]],.]]=>[[.,[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]],.]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]],.]]=>[[.,[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]],.]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]],.]]=>[[.,[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]],.]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]],.]]=>[[.,[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]],.]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.],.]]=>[[.,[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]],.]
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.],.]]=>[[.,[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]],.]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.],.]]=>[[.,[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]],.]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.],.]]=>[[.,[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]],.]
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.],.]]=>[[.,[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]]],.]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.],.]]=>[[.,[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]]],.]
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.],.]]=>[[.,[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]]],.]
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.],.]]=>[[.,[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]]],.]
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.],.]]=>[[.,[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]]],.]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.],.]]=>[[.,[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]],.]
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.],.]]=>[[.,[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]],.]
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.],.]]=>[[.,[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]],.]
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.],.]]=>[[.,[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]],.]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.],.]]=>[[.,[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]],.]
          
Map
to binary tree: left tree, up step, right tree, down step
Description
Return the binary tree corresponding to the Dyck path under the transformation left tree - up step - right tree - down step.
A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ for Dyck paths $L,R$ of respective semilengths $n_1,n_2$ with $n_1+n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.
Map
left-right symmetry
Description
Return the left-right symmetrized tree of a binary tree.