FindStat - MapsDatabase

edit this map or download as text // json

Identifier

Mp00140: Dyck paths —logarithmic height to pruning number⟶ Binary trees

Images

=>
            
              Cc0005;cc-rep-0Cc0010;cc-rep-1
            

            [1,0]=>[.,.]
[1,0,1,0]=>[.,[.,.]]
[1,1,0,0]=>[[.,.],.]
[1,0,1,0,1,0]=>[.,[.,[.,.]]]
[1,0,1,1,0,0]=>[.,[[.,.],.]]
[1,1,0,0,1,0]=>[[.,[.,.]],.]
[1,1,0,1,0,0]=>[[[.,.],.],.]
[1,1,1,0,0,0]=>[[.,.],[.,.]]
[1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0]=>[.,[.,[[.,.],.]]]
[1,0,1,1,0,0,1,0]=>[.,[[.,[.,.]],.]]
[1,0,1,1,0,1,0,0]=>[.,[[[.,.],.],.]]
[1,0,1,1,1,0,0,0]=>[.,[[.,.],[.,.]]]
[1,1,0,0,1,0,1,0]=>[[.,[.,[.,.]]],.]
[1,1,0,0,1,1,0,0]=>[[.,[[.,.],.]],.]
[1,1,0,1,0,0,1,0]=>[[[.,[.,.]],.],.]
[1,1,0,1,0,1,0,0]=>[[[[.,.],.],.],.]
[1,1,0,1,1,0,0,0]=>[[[.,.],[.,.]],.]
[1,1,1,0,0,0,1,0]=>[[.,.],[.,[.,.]]]
[1,1,1,0,0,1,0,0]=>[[.,.],[[.,.],.]]
[1,1,1,0,1,0,0,0]=>[[.,[.,.]],[.,.]]
[1,1,1,1,0,0,0,0]=>[[[.,.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0]=>[.,[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,0]=>[.,[.,[[.,[.,.]],.]]]
[1,0,1,0,1,1,0,1,0,0]=>[.,[.,[[[.,.],.],.]]]
[1,0,1,0,1,1,1,0,0,0]=>[.,[.,[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,0,1,0]=>[.,[[.,[.,[.,.]]],.]]
[1,0,1,1,0,0,1,1,0,0]=>[.,[[.,[[.,.],.]],.]]
[1,0,1,1,0,1,0,0,1,0]=>[.,[[[.,[.,.]],.],.]]
[1,0,1,1,0,1,0,1,0,0]=>[.,[[[[.,.],.],.],.]]
[1,0,1,1,0,1,1,0,0,0]=>[.,[[[.,.],[.,.]],.]]
[1,0,1,1,1,0,0,0,1,0]=>[.,[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,0]=>[.,[[.,.],[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,0]=>[.,[[.,[.,.]],[.,.]]]
[1,0,1,1,1,1,0,0,0,0]=>[.,[[[.,.],.],[.,.]]]
[1,1,0,0,1,0,1,0,1,0]=>[[.,[.,[.,[.,.]]]],.]
[1,1,0,0,1,0,1,1,0,0]=>[[.,[.,[[.,.],.]]],.]
[1,1,0,0,1,1,0,0,1,0]=>[[.,[[.,[.,.]],.]],.]
[1,1,0,0,1,1,0,1,0,0]=>[[.,[[[.,.],.],.]],.]
[1,1,0,0,1,1,1,0,0,0]=>[[.,[[.,.],[.,.]]],.]
[1,1,0,1,0,0,1,0,1,0]=>[[[.,[.,[.,.]]],.],.]
[1,1,0,1,0,0,1,1,0,0]=>[[[.,[[.,.],.]],.],.]
[1,1,0,1,0,1,0,0,1,0]=>[[[[.,[.,.]],.],.],.]
[1,1,0,1,0,1,0,1,0,0]=>[[[[[.,.],.],.],.],.]
[1,1,0,1,0,1,1,0,0,0]=>[[[[.,.],[.,.]],.],.]
[1,1,0,1,1,0,0,0,1,0]=>[[[.,.],[.,[.,.]]],.]
[1,1,0,1,1,0,0,1,0,0]=>[[[.,.],[[.,.],.]],.]
[1,1,0,1,1,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],.]
[1,1,0,1,1,1,0,0,0,0]=>[[[[.,.],.],[.,.]],.]
[1,1,1,0,0,0,1,0,1,0]=>[[.,.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0]=>[[.,.],[.,[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,0]=>[[.,.],[[.,[.,.]],.]]
[1,1,1,0,0,1,0,1,0,0]=>[[.,.],[[[.,.],.],.]]
[1,1,1,0,0,1,1,0,0,0]=>[[.,.],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,0,1,0]=>[[.,[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,.],.]]
[1,1,1,0,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[.,.]]
[1,1,1,0,1,1,0,0,0,0]=>[[.,[[.,.],.]],[.,.]]
[1,1,1,1,0,0,0,0,1,0]=>[[[.,.],.],[.,[.,.]]]
[1,1,1,1,0,0,0,1,0,0]=>[[[.,.],.],[[.,.],.]]
[1,1,1,1,0,0,1,0,0,0]=>[[[.,[.,.]],.],[.,.]]
[1,1,1,1,0,1,0,0,0,0]=>[[[[.,.],.],.],[.,.]]
[1,1,1,1,1,0,0,0,0,0]=>[[[.,.],[.,.]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[.,[.,[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[.,[.,[.,[[.,[.,.]],.]]]]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[.,[.,[.,[[[.,.],.],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[.,[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[.,[.,[[.,[.,[.,.]]],.]]]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[.,[.,[[.,[[.,.],.]],.]]]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[.,[.,[[[.,[.,.]],.],.]]]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[.,[.,[[[[.,.],.],.],.]]]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[.,[.,[[[.,.],[.,.]],.]]]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[.,[.,[[.,.],[[.,.],.]]]]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[.,[.,[[.,[.,.]],[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[.,[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[.,[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[.,[[.,[.,[[.,.],.]]],.]]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[.,[[.,[[.,[.,.]],.]],.]]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[.,[[.,[[[.,.],.],.]],.]]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[.,[[.,[[.,.],[.,.]]],.]]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[.,[[[.,[.,[.,.]]],.],.]]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[.,[[[.,[[.,.],.]],.],.]]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[.,[[[[.,[.,.]],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,.],.],.],.],.]]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[.,[[[[.,.],[.,.]],.],.]]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[.,[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[.,[[[.,.],[[.,.],.]],.]]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[.,[[[.,[.,.]],[.,.]],.]]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[.,[[[[.,.],.],[.,.]],.]]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[.,[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[.,[[.,.],[[[.,.],.],.]]]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[.,[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[.,[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[.,[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[.,[[.,[[.,.],.]],[.,.]]]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[.,[[[.,.],.],[[.,.],.]]]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[.,[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[.,[[[[.,.],.],.],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[[.,[.,[.,[.,[.,.]]]]],.]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[[.,[.,[.,[[.,.],.]]]],.]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[[.,[.,[[.,[.,.]],.]]],.]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[[.,[.,[[[.,.],.],.]]],.]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[[.,[.,[[.,.],[.,.]]]],.]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[[.,[[.,[.,[.,.]]],.]],.]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[[.,[[.,.],.]],.]],.]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[[.,[[[.,[.,.]],.],.]],.]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[[[[.,.],.],.],.]],.]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[[[.,.],[.,.]],.]],.]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[[.,[[.,.],[.,[.,.]]]],.]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,.],[[.,.],.]]],.]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[[.,[.,.]],[.,.]]],.]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[[[.,.],.],[.,.]]],.]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[[[.,[.,[.,[.,.]]]],.],.]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[[[.,[.,[[.,.],.]]],.],.]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,[.,.]],.]],.],.]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[[[.,[[[.,.],.],.]],.],.]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[[[.,[[.,.],[.,.]]],.],.]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[[[[.,[.,[.,.]]],.],.],.]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[[[[.,[[.,.],.]],.],.],.]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[[[[[.,[.,.]],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[[[[[[.,.],.],.],.],.],.]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[[[[[.,.],[.,.]],.],.],.]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[[[[.,.],[.,[.,.]]],.],.]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[[[[.,.],[[.,.],.]],.],.]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[[[[.,[.,.]],[.,.]],.],.]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[[[[[.,.],.],[.,.]],.],.]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[[.,.],.]]],.]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,.]],.]],.]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[[[.,.],[[[.,.],.],.]],.]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[[[.,.],[[.,.],[.,.]]],.]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[[[.,[.,.]],[[.,.],.]],.]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,.]]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[[[.,[[.,.],.]],[.,.]],.]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[[[[.,.],.],[.,[.,.]]],.]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[[[[.,.],.],[[.,.],.]],.]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[[[[.,[.,.]],.],[.,.]],.]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[[[[[.,.],.],.],[.,.]],.]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,.]],.]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[[.,.],[.,[[.,[.,.]],.]]]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[[.,.],[.,[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[[.,.],[[.,[.,[.,.]]],.]]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[.,[[.,.],.]],.]]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[[.,.],[[[.,[.,.]],.],.]]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[[.,.],[[[[.,.],.],.],.]]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,.],[.,.]],.]]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[[.,.],[[[.,.],.],[.,.]]]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[.,.]],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,.],.],.]]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[[.,[.,[.,.]]],[[.,.],.]]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[[.,[.,[[.,.],.]]],[.,.]]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[[.,.],.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,.],.]]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[[.,[[.,[.,.]],.]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[[[.,.],.],.]],[.,.]]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[[.,[[.,.],[.,.]]],[.,.]]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],.],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[[[.,.],.],[[.,[.,.]],.]]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[[[.,.],.],[[[.,.],.],.]]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[[[.,.],.],[[.,.],[.,.]]]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[.,.],.]]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[[[.,[.,[.,.]]],.],[.,.]]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[[[.,[[.,.],.]],.],[.,.]]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[[[[.,.],.],.],[[.,.],.]]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[[[[.,[.,.]],.],.],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[[[[[.,.],.],.],.],[.,.]]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[[[[.,.],[.,.]],.],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[[[.,.],[[.,.],.]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[[[.,.],[.,.]],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[.,[.,[.,[[[[.,.],.],.],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[.,[.,[[.,[[.,[.,.]],.]],.]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[.,[.,[[.,[[[.,.],.],.]],.]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[.,[.,[[[.,[[.,.],.]],.],.]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[.,[.,[[[[.,[.,.]],.],.],.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[.,[.,[[[[[.,.],.],.],.],.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[.,[.,[[[[.,.],[.,.]],.],.]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[.,[.,[[[.,.],[[.,.],.]],.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[.,[.,[[[[.,.],.],[.,.]],.]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[.,[.,[[.,.],[[[.,.],.],.]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[.,[.,[[[.,.],.],[[.,.],.]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[.,[.,[[[[.,.],.],.],[.,.]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[.,[[.,[.,[[.,[.,.]],.]]],.]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[.,[[.,[.,[[[.,.],.],.]]],.]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[.,[[.,[[.,[.,[.,.]]],.]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[.,[[.,[[.,[[.,.],.]],.]],.]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[.,[[.,[[[.,[.,.]],.],.]],.]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[.,[[.,[[[[.,.],.],.],.]],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[.,[[.,[[[.,.],[.,.]],.]],.]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,.],.]]],.]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[.,[[.,[[[.,.],.],[.,.]]],.]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[.,[[[.,[.,[.,[.,.]]]],.],.]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[.,[[[.,[.,[[.,.],.]]],.],.]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[.,[[[.,[[.,[.,.]],.]],.],.]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[.,[[[.,[[[.,.],.],.]],.],.]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],.]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[.,[[[[.,[.,[.,.]]],.],.],.]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[.,[[[[.,[[.,.],.]],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[.,[[[[[.,[.,.]],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[.,.],[.,.]],.],.],.]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[.,[[[[.,.],[.,[.,.]]],.],.]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[.,.],[[.,.],.]],.],.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[.,[.,.]],[.,.]],.],.]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[[.,.],.],[.,.]],.],.]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[.,[[[.,.],[.,[[.,.],.]]],.]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[.,[[[.,.],[[.,[.,.]],.]],.]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[[.,.],[[[.,.],.],.]],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,.],.]],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,[[.,.],.]],[.,.]],.]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[.,[[[[.,.],.],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[[[.,.],.],[[.,.],.]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[[.,[.,.]],.],[.,.]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[[[[.,.],.],.],[.,.]],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[[[.,.],[.,.]],[.,.]],.]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[.,[[.,.],[.,[[[.,.],.],.]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[.,[[.,.],[[.,[[.,.],.]],.]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[.,[[.,.],[[[.,[.,.]],.],.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[.,.],[[[[.,.],.],.],.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[.,[.,.]],[[[.,.],.],.]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[.,.],.]],[[.,.],.]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[.,[[[.,.],.],.]],[.,.]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[.,[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[.,[[[.,.],.],[[.,[.,.]],.]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[.,[[[.,.],.],[[[.,.],.],.]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],.],[[.,.],.]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[.,[[[.,[[.,.],.]],.],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[.,[[[[.,.],.],.],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[[[.,.],.],.],[[.,.],.]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[[[.,[.,.]],.],.],[.,.]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[.,[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[.,[[[[.,.],[.,.]],.],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[.,[[[[.,.],.],[.,.]],[.,.]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[.,[.,[.,[[[.,.],.],.]]]],.]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[.,[.,[[.,[[.,.],.]],.]]],.]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[.,[.,[[[.,[.,.]],.],.]]],.]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[.,[.,[[[[.,.],.],.],.]]],.]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[.,[.,[[[.,.],[.,.]],.]]],.]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[.,[.,[[.,.],[[.,.],.]]]],.]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[.,[.,[[[.,.],.],[.,.]]]],.]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[.,[[.,[.,[[.,.],.]]],.]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[.,[[.,[[.,[.,.]],.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[[.,.],.],.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[.,[[.,[[.,.],[.,.]]],.]],.]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[.,[[[.,[.,[.,.]]],.],.]],.]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[.,[[[.,[[.,.],.]],.],.]],.]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[.,[[[[.,[.,.]],.],.],.]],.]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[[[[[.,.],.],.],.],.]],.]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,[[[[.,.],[.,.]],.],.]],.]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[.,[[[.,.],[.,[.,.]]],.]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[[[.,.],[[.,.],.]],.]],.]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],.]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[[[[.,.],.],[.,.]],.]],.]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[.,[[.,.],.]]]],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[.,[[.,.],[[.,[.,.]],.]]],.]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[.,[[.,.],[[[.,.],.],.]]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,[.,.]],[[.,.],.]]],.]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[.,[[.,[[.,.],.]],[.,.]]],.]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[.,[[[.,.],.],[.,[.,.]]]],.]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[.,[[[.,.],.],[[.,.],.]]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[.,[[[.,[.,.]],.],[.,.]]],.]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[.,[[[[.,.],.],.],[.,.]]],.]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],[.,.]]],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[.,[.,[.,[[.,.],.]]]],.],.]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[.,[.,[[.,[.,.]],.]]],.],.]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[.,[.,[[[.,.],.],.]]],.],.]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,[[.,.],[.,.]]]],.],.]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[.,[[.,[.,[.,.]]],.]],.],.]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,[[.,.],.]],.]],.],.]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[[.,[.,.]],.],.]],.],.]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[[.,[[[[.,.],.],.],.]],.],.]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,[[[.,.],[.,.]],.]],.],.]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,[[.,.],[.,[.,.]]]],.],.]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[[.,.],[[.,.],.]]],.],.]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,[[.,[.,.]],[.,.]]],.],.]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,[[[.,.],.],[.,.]]],.],.]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,[.,.]]]],.],.],.]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[[.,[.,[[.,.],.]]],.],.],.]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[[.,[[.,[.,.]],.]],.],.],.]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[[[.,[[[.,.],.],.]],.],.],.]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[[[.,[[.,.],[.,.]]],.],.],.]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[[[.,[.,[.,.]]],.],.],.],.]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[[[.,[[.,.],.]],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[[[[.,[.,.]],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[[[[.,.],.],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[[[[.,.],[.,.]],.],.],.],.]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[[[[.,.],[.,[.,.]]],.],.],.]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[[[[.,.],[[.,.],.]],.],.],.]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[[[.,[.,.]],[.,.]],.],.],.]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[[[[[.,.],.],[.,.]],.],.],.]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,[.,.]]]],.],.]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[[[.,.],[.,[[.,.],.]]],.],.]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[[[.,.],[[.,[.,.]],.]],.],.]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[[[.,.],[[[.,.],.],.]],.],.]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[[[.,.],[[.,.],[.,.]]],.],.]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[[[.,[.,.]],[.,[.,.]]],.],.]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[[.,.],.]],.],.]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[[[.,[.,[.,.]]],[.,.]],.],.]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[[.,[[.,.],.]],[.,.]],.],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[[[[.,.],.],[[.,.],.]],.],.]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[[[.,[.,.]],.],[.,.]],.],.]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[[[[[.,.],.],.],[.,.]],.],.]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,.],[.,[.,[[.,.],.]]]],.]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,.],[.,[[.,[.,.]],.]]],.]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[[[.,.],.],.]]],.]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[.,.],[[.,[.,[.,.]]],.]],.]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,[[.,.],.]],.]],.]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[[.,[.,.]],.],.]],.]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[[.,.],[[[[.,.],.],.],.]],.]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[[.,.],[[[.,.],[.,.]],.]],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,.],[[.,.],[[.,.],.]]],.]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[[.,.],[[.,[.,.]],[.,.]]],.]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[[.,.],[[[.,.],.],[.,.]]],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[[.,.],.]]],.]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,[.,.]],.]],.]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[[.,[.,.]],[[[.,.],.],.]],.]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[[.,[.,.]],[[.,.],[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[[.,[.,[.,.]]],[[.,.],.]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[[.,[.,[[.,.],.]]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,[[.,.],.]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[[.,[[.,.],.]],[[.,.],.]],.]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,[[[.,.],.],.]],[.,.]],.]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[[.,[[.,.],[.,.]]],[.,.]],.]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[[[.,.],.],[.,[[.,.],.]]],.]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[[[.,.],.],[[.,[.,.]],.]],.]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[[[.,.],.],[[[.,.],.],.]],.]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[[[.,[.,.]],.],[.,[.,.]]],.]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],.],[[.,.],.]],.]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[[[.,[.,[.,.]]],.],[.,.]],.]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[[[.,[[.,.],.]],.],[.,.]],.]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[[[[.,.],.],.],[[.,.],.]],.]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[[[.,[.,.]],.],.],[.,.]],.]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[[[[[.,.],.],.],.],[.,.]],.]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[[[.,.],[[.,.],.]],[.,.]],.]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[.,[[.,[[.,.],.]],.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[.,.],[.,[[[.,[.,.]],.],.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[.,.],[.,[[[[.,.],.],.],.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[.,.],[[.,[.,[[.,.],.]]],.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[.,.],[[.,[[.,[.,.]],.]],.]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,.],[[.,[[[.,.],.],.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[.,.],[[.,[[.,.],[.,.]]],.]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[.,.],[[[.,[.,[.,.]]],.],.]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[.,.],[[[.,[[.,.],.]],.],.]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[.,.],[[[[.,[.,.]],.],.],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[.,.],.],.],.],.]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[.,.],[.,.]],.],.]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,.],.]],.]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[.,[.,.]],[.,.]],.]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[.,.],[[[[.,.],.],[.,.]],.]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[.,.],[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[.,.]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[.,.]],[[[.,[.,.]],.],.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[[.,.],.],.]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[.,[.,[[.,.],.]]],[[.,.],.]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,[[[.,.],.],.]]],[.,.]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[[.,.],.]],[.,[[.,.],.]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[.,.],.]],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,.],.]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[.,[[.,[[.,.],.]],.]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[[[.,.],.],.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[[[.,.],.],.]],[[.,.],.]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[.,[[[.,[.,.]],.],.]],[.,.]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[.,[[[[.,.],.],.],.]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],.]],[.,.]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[.,.]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[.,[[[.,.],.],[.,.]]],[.,.]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,.],.],[.,[[.,[.,.]],.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[.,.],.],[[.,[.,[.,.]]],.]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[[.,.],.],[[.,[[.,.],.]],.]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[.,.],.],[[[.,[.,.]],.],.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[[[.,.],.],.],.]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[[.,.],.],[[[.,.],[.,.]],.]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[[.,[.,[.,.]]],.],[[.,.],.]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[[.,[.,[[.,.],.]]],.],[.,.]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[[.,[[.,.],.]],.],[.,[.,.]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[[.,[[.,[.,.]],.]],.],[.,.]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[[[.,[[[.,.],.],.]],.],[.,.]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[[.,[[.,.],[.,.]]],.],[.,.]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[[.,.],.],.],[[.,[.,.]],.]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[[.,.],.],.],[[[.,.],.],.]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[[[.,[.,[.,.]]],.],.],[.,.]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[[.,[[.,.],.]],.],.],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[[[[.,.],.],.],.],[[.,.],.]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[[[.,.],[[.,.],.]],.],[.,.]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,.]],.]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[[.,[[.,.],.]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[.,[.,[.,[[[[[.,.],.],.],.],.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[.,[.,[[.,[[[[.,.],.],.],.]],.]]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[.,[.,[[[.,[[.,[.,.]],.]],.],.]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[.,[.,[[[.,[[[.,.],.],.]],.],.]]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[.,[.,[[[[.,[[.,.],.]],.],.],.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[.,[.,[[[[[.,[.,.]],.],.],.],.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[.,[.,[[[[[[.,.],.],.],.],.],.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[.,[.,[[[[[.,.],[.,.]],.],.],.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[.,[.,[[[[.,.],[[.,.],.]],.],.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[.,[.,[[[[[.,.],.],[.,.]],.],.]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[.,[.,[[[.,.],[[[.,.],.],.]],.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[.,[.,[[[.,[.,.]],[[.,.],.]],.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[.,[.,[[[[.,.],.],[[.,.],.]],.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[.,[.,[[[[[.,.],.],.],[.,.]],.]]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[.,[.,[[[[.,.],.],.],[[.,.],.]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[.,[.,[[[[[.,.],.],.],.],[.,.]]]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[.,[.,[[[[.,.],.],[.,.]],[.,.]]]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[.,[[.,[.,[[[[.,.],.],.],.]]],.]]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[.,[[.,[.,[[.,.],[[.,.],.]]]],.]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[.,[[.,[[.,[[[.,.],.],.]],.]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[.,[[.,[[[.,[[.,.],.]],.],.]],.]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[.,[[.,[[[[.,[.,.]],.],.],.]],.]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[.,[[.,[[[[[.,.],.],.],.],.]],.]]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[.,[[.,[[[[.,.],[.,.]],.],.]],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[.,[[.,[[[.,.],[[.,.],.]],.]],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[.,[[.,[[[[.,.],.],[.,.]],.]],.]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[.,[[.,[[.,.],[.,[[.,.],.]]]],.]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[.,[[.,[[.,.],[[[.,.],.],.]]],.]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[.,[[.,[[[.,.],.],[[.,.],.]]],.]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[.,[[.,[[[[.,.],.],.],[.,.]]],.]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[.,[[[.,[.,[.,[[.,.],.]]]],.],.]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[.,[[[.,[.,[[[.,.],.],.]]],.],.]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[.,[[[.,[.,[[.,.],[.,.]]]],.],.]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[.,[[[.,[[.,[[.,.],.]],.]],.],.]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[.,[[[.,[[[.,[.,.]],.],.]],.],.]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[.,[[[.,[[[[.,.],.],.],.]],.],.]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[.,[[[.,[[[.,.],[.,.]],.]],.],.]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[.,[[[.,[[.,.],[[.,.],.]]],.],.]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[.,[[[.,[[[.,.],.],[.,.]]],.],.]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[.,[[[[.,[.,[[.,.],.]]],.],.],.]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[.,[[[[.,[[.,[.,.]],.]],.],.],.]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[.,[[[[.,[[[.,.],.],.]],.],.],.]]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[.,[[[[.,[[.,.],[.,.]]],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[.,[[[[[.,[.,[.,.]]],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[.,[[[[[.,[[.,.],.]],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[.,[[[[[[.,[.,.]],.],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[[.,.],[.,.]],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[.,[[[[[.,.],[.,[.,.]]],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[.,.],[[.,.],.]],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[[.,[.,.]],[.,.]],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[[[.,.],.],[.,.]],.],.],.]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[.,[[[[.,.],[.,[[.,.],.]]],.],.]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[.,[[[[.,.],[[.,[.,.]],.]],.],.]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[.,.],[[[.,.],.],.]],.],.]]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[.,.],[[.,.],[.,.]]],.],.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[[.,.],.]],.],.]]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[[.,[[.,.],.]],[.,.]],.],.]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[.,[[[[[.,.],.],[.,[.,.]]],.],.]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[[[[.,.],.],[[.,.],.]],.],.]]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[[[.,[.,.]],.],[.,.]],.],.]]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[[[[[.,.],.],.],[.,.]],.],.]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[[[[.,.],[.,.]],[.,.]],.],.]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[.,[[[.,.],[.,[[[.,.],.],.]]],.]]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[.,[[[.,.],[[.,[[.,.],.]],.]],.]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[.,[[[.,.],[[[.,[.,.]],.],.]],.]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[.,.],[[[[.,.],.],.],.]],.]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,.],[[[.,.],[.,.]],.]],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[[.,.],.]]],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[[.,.],[[[.,.],.],[.,.]]],.]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[.,.]],[[[.,.],.],.]],.]]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[.,[[[.,[.,[[.,.],.]]],[.,.]],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[[.,.],.]],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[[.,[[[.,.],.],.]],[.,.]],.]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[.,[[[[.,.],.],[.,[[.,.],.]]],.]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[.,[[[[.,.],.],[[.,[.,.]],.]],.]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[.,[[[[.,.],.],[[[.,.],.],.]],.]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[.,[[[[.,.],.],[[.,.],[.,.]]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],.],[[.,.],.]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[.,[[[[.,[[.,.],.]],.],[.,.]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[[[[.,.],.],.],[[.,.],.]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[[[[.,[.,.]],.],.],[.,.]],.]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[.,[[[[[[.,.],.],.],.],[.,.]],.]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[.,[[[[[.,.],[.,.]],.],[.,.]],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[.,[[[[.,.],[[.,.],.]],[.,.]],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[.,[[[[[.,.],.],[.,.]],[.,.]],.]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[[[.,.],[.,.]],[[.,.],.]],.]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[.,[[.,.],[[.,[[[.,.],.],.]],.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[.,[[.,.],[[[.,[[.,.],.]],.],.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[.,[[.,.],[[[[.,[.,.]],.],.],.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[.,.],[[[[[.,.],.],.],.],.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[.,[[.,.],[[[[.,.],[.,.]],.],.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[.,[[.,.],[[[.,.],[[.,.],.]],.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[.,[[.,.],[[[[.,.],.],[.,.]],.]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[.,[[.,.],[[[[.,.],.],.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[.,[.,.]],[[[[.,.],.],.],.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[.,[[.,[[.,.],.]],[[[.,.],.],.]]]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[.,[[.,[[[.,.],.],.]],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[.,[[[.,.],.],.]],[[.,.],.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[.,[[.,[[[[.,.],.],.],.]],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[.,[[[.,.],.],[[.,[[.,.],.]],.]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[.,[[[.,.],.],[[[.,[.,.]],.],.]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,.],.],[[[.,.],[.,.]],.]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[.,.]],.],[[[.,.],.],.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],.],[[.,.],.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[.,[[[.,[[.,[.,.]],.]],.],[.,.]]]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[.,[[[.,[[[.,.],.],.]],.],[.,.]]]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[.,[[[[.,.],.],.],[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[.,[[[[.,.],.],.],[[.,[.,.]],.]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[.,[[[[.,[[.,.],.]],.],.],[.,.]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[.,[[[[[.,[.,.]],.],.],.],[.,.]]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[.,[[[[[.,.],[.,.]],.],.],[.,.]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[.,[[[[.,.],[[.,.],.]],.],[.,.]]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[.,[[[[[.,.],.],[.,.]],.],[.,.]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[.,[[[[.,.],[.,.]],.],[[.,.],.]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[.,[[[.,.],[[[.,.],.],.]],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[[[.,.],.],[[.,.],.]],[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[.,[[[[[.,.],.],.],[.,.]],[.,.]]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],.]],[[.,.],.]]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[.,[[[[.,.],.],[.,.]],[[.,.],.]]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],.]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[.,[.,[[.,[[[.,.],.],.]],.]]],.]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[.,[.,[[[.,[[.,.],.]],.],.]]],.]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[.,[.,[[[[.,[.,.]],.],.],.]]],.]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,[[[[[.,.],.],.],.],.]]],.]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[.,[.,[[[[.,.],[.,.]],.],.]]],.]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[.,[[[.,.],[[.,.],.]],.]]],.]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[.,[[[[.,.],.],[.,.]],.]]],.]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[.,[.,[[.,.],[[[.,.],.],.]]]],.]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[.,[.,[[[.,.],.],[[.,.],.]]]],.]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[.,[.,[[[[.,.],.],.],[.,.]]]],.]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[.,[[.,[.,[[[.,.],.],.]]],.]],.]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[.,[[.,[.,[[.,.],[.,.]]]],.]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[.,[[.,[[[.,[.,.]],.],.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[[.,[[[[.,.],.],.],.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,[[[.,.],[.,.]],.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[[.,[[[.,.],.],[.,.]]],.]],.]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[.,[[[.,[.,[[.,.],.]]],.],.]],.]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[.,[[[.,[[.,[.,.]],.]],.],.]],.]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[[[.,[[[.,.],.],.]],.],.]],.]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[[[.,[[.,.],[.,.]]],.],.]],.]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[.,[[[[.,[.,[.,.]]],.],.],.]],.]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[[.,[[.,.],.]],.],.],.]],.]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[.,[.,.]],.],.],.],.]],.]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[[[[[[.,.],.],.],.],.],.]],.]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[.,[[[[[.,.],[.,.]],.],.],.]],.]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[[.,.],[.,[.,.]]],.],.]],.]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[.,[[[[.,.],[[.,.],.]],.],.]],.]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[[[[.,[.,.]],[.,.]],.],.]],.]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[.,[[[[[.,.],.],[.,.]],.],.]],.]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[.,.],[.,[[.,.],.]]],.]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[.,[[[.,.],[[[.,.],.],.]],.]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[[[.,.],[[.,.],[.,.]]],.]],.]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],[[.,.],.]],.]],.]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[[[.,[[.,.],.]],[.,.]],.]],.]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[[[[.,.],.],[.,[.,.]]],.]],.]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[.,[[[[.,.],.],[[.,.],.]],.]],.]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[.,[[[[.,[.,.]],.],[.,.]],.]],.]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[.,[[[[[.,.],.],.],[.,.]],.]],.]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[.,[[[[.,.],[.,.]],[.,.]],.]],.]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[.,[[.,.],[.,[[.,[.,.]],.]]]],.]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[.,[[[.,.],.],.]]]],.]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],.]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[[.,.],[[[.,[.,.]],.],.]]],.]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[.,[[.,.],[[[[.,.],.],.],.]]],.]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[.,[[.,.],[[[.,.],[.,.]],.]]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[.,[[.,.],[[[.,.],.],[.,.]]]],.]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[.,[[.,[.,.]],[[[.,.],.],.]]],.]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],.]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[[.,[[[.,.],.],.]],[.,.]]],.]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[[[.,.],.],[.,[[.,.],.]]]],.]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],.],[[.,[.,.]],.]]],.]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],.],[[.,.],.]]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[.,[[[.,[[.,.],.]],.],[.,.]]],.]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[.,[[[[.,.],.],.],[[.,.],.]]],.]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[.,[[[[.,[.,.]],.],.],[.,.]]],.]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[.,[[[[[.,.],.],.],.],[.,.]]],.]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[.,[[[[.,.],[.,.]],.],[.,.]]],.]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[.,[[[[.,.],.],[.,.]],[.,.]]],.]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],[[.,.],.]]],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[.,[.,[.,[[[.,.],.],.]]]],.],.]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[.,[.,[.,[[.,.],[.,.]]]]],.],.]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[.,[.,[[.,[[.,.],.]],.]]],.],.]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[.,[.,[[[.,[.,.]],.],.]]],.],.]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,[.,[[[[.,.],.],.],.]]],.],.]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,[.,[[[.,.],[.,.]],.]]],.],.]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,[.,[[.,.],[[.,.],.]]]],.],.]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,[.,[[[.,.],.],[.,.]]]],.],.]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[.,[[.,[.,[[.,.],.]]],.]],.],.]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[[.,[[[.,.],.],.]],.]],.],.]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,[[.,[[.,.],[.,.]]],.]],.],.]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,[[[[.,[.,.]],.],.],.]],.],.]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,[[[[[.,.],.],.],.],.]],.],.]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[[.,[[[[.,.],[.,.]],.],.]],.],.]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,[[[.,.],[.,[.,.]]],.]],.],.]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[[.,[[[.,.],[[.,.],.]],.]],.],.]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],.],.]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[[.,[[[[.,.],.],[.,.]],.]],.],.]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[.,[[.,.],[.,[.,[.,.]]]]],.],.]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,[[.,.],[.,[[.,.],.]]]],.],.]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,[[.,.],[[.,[.,.]],.]]],.],.]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[[.,[[.,.],[[[.,.],.],.]]],.],.]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[[.,[[.,.],[[.,.],[.,.]]]],.],.]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],[[.,.],.]]],.],.]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[[.,[[.,[[.,.],.]],[.,.]]],.],.]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[[[.,.],.],[.,[.,.]]]],.],.]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[[.,[[[.,.],.],[[.,.],.]]],.],.]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[[.,[[[.,[.,.]],.],[.,.]]],.],.]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[[.,[[[[.,.],.],.],[.,.]]],.],.]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,[[[.,.],[.,.]],[.,.]]],.],.]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[.,[.,[[.,.],.]]]],.],.],.]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,[[.,[.,.]],.]]],.],.],.]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[[.,[.,[[[.,.],.],.]]],.],.],.]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[[.,[.,[[.,.],[.,.]]]],.],.],.]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[[[.,[[[.,.],[.,.]],.]],.],.],.]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[[.,[[.,.],[.,[.,.]]]],.],.],.]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[[.,[[.,.],[[.,.],.]]],.],.],.]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[[[.,[[.,[.,.]],[.,.]]],.],.],.]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[[[.,[[[.,.],.],[.,.]]],.],.],.]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[[[.,[.,[[.,.],.]]],.],.],.],.]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[[[[.,[[.,.],[.,.]]],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[[[[.,.],[.,[[.,.],.]]],.],.],.]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[[[[.,.],[[.,[.,.]],.]],.],.],.]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[[[[.,.],[[[.,.],.],.]],.],.],.]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[[[[.,.],[[.,.],[.,.]]],.],.],.]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[[[[.,[.,.]],[[.,.],.]],.],.],.]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],.]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[[[.,[[.,.],.]],[.,.]],.],.],.]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[[[[[.,.],.],[[.,.],.]],.],.],.]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[[[[.,[.,.]],.],[.,.]],.],.],.]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[.,[.,[[.,.],.]]]],.],.]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,[[.,[.,.]],.]]],.],.]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[[[.,.],[.,[[[.,.],.],.]]],.],.]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[[[.,.],[.,[[.,.],[.,.]]]],.],.]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[[.,.],[[.,[.,[.,.]]],.]],.],.]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[[.,.],[[.,[[.,.],.]],.]],.],.]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[[[.,.],[[[.,[.,.]],.],.]],.],.]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[[[.,.],[[[[.,.],.],.],.]],.],.]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[[[.,.],[[[.,.],[.,.]],.]],.],.]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[[[.,.],[[.,[.,.]],[.,.]]],.],.]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[[[.,.],[[[.,.],.],[.,.]]],.],.]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],.],.]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[[[.,[.,.]],[[[.,.],.],.]],.],.]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[[[.,[.,.]],[[.,.],[.,.]]],.],.]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[[[.,[.,[.,.]]],[[.,.],.]],.],.]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[[[.,[.,[[.,.],.]]],[.,.]],.],.]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[[.,[[.,.],.]],[.,[.,.]]],.],.]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[[[.,[[.,.],.]],[[.,.],.]],.],.]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[[[.,[[.,[.,.]],.]],[.,.]],.],.]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[[.,[[[.,.],.],.]],[.,.]],.],.]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[[[.,[[.,.],[.,.]]],[.,.]],.],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[[[[.,.],.],[.,[[.,.],.]]],.],.]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[[[[.,.],.],[[.,[.,.]],.]],.],.]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[[[[.,.],.],[[.,.],[.,.]]],.],.]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[[[[.,[.,.]],.],[.,[.,.]]],.],.]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[[[.,[.,.]],.],[[.,.],.]],.],.]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],.]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[[[[.,[[.,.],.]],.],[.,.]],.],.]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[[[[.,.],[[.,.],.]],[.,.]],.],.]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],[[.,.],.]],.],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,.],[.,[.,[[[.,.],.],.]]]],.]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[.,.],[.,[[.,[.,[.,.]]],.]]],.]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],[.,[[.,[[.,.],.]],.]]],.]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,.],[.,[[[.,[.,.]],.],.]]],.]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],[.,[[[[.,.],.],.],.]]],.]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[.,[[[.,.],[.,.]],.]]],.]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],[.,[[.,.],[[.,.],.]]]],.]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,[[[.,.],.],[.,.]]]],.]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,.],[[.,[.,[[.,.],.]]],.]],.]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,.],[[.,[[.,[.,.]],.]],.]],.]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,[[[.,.],.],.]],.]],.]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],[[.,[[.,.],[.,.]]],.]],.]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[.,.],[[[.,[.,[.,.]]],.],.]],.]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[[[.,[[.,.],.]],.],.]],.]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[.,[.,.]],.],.],.]],.]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[[.,.],[[[[.,.],[.,.]],.],.]],.]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],.]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[[.,.],[[[.,.],[[.,.],.]],.]],.]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],.]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[[.,.],[[[[.,.],.],[.,.]],.]],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],[.,[[.,.],.]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,.],[[.,[.,.]],.]]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[[.,.],[[.,[.,.]],[[.,.],.]]],.]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[.,.],[[.,[[.,.],.]],[.,.]]],.]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[[.,.],[[[.,.],.],[.,[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[.,.],[[[.,.],.],[[.,.],.]]],.]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[[.,.],[[[.,[.,.]],.],[.,.]]],.]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[[.,.],[[[[.,.],.],.],[.,.]]],.]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[.,[[[.,.],.],.]]],.]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,[[.,.],.]],.]],.]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[[.,[.,.]],[[[[.,.],.],.],.]],.]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[[.,[.,.]],[[[.,.],[.,.]],.]],.]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[[.,[.,.]],[[[.,.],.],[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[[.,[.,[.,.]]],[[[.,.],.],.]],.]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[[.,[.,[[.,.],.]]],[[.,.],.]],.]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[[.,[.,[[[.,.],.],.]]],[.,.]],.]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],.]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],.]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[[.,[[.,.],.]],[[[.,.],.],.]],.]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[[.,[[.,.],.]],[[.,.],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[[.,.],.]],.]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[[.,[[[.,.],.],.]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,[[[.,.],.],.]],[[.,.],.]],.]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[[.,[[[.,[.,.]],.],.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[[.,[[[[.,.],.],.],.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[[.,[[[.,.],[.,.]],.]],[.,.]],.]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[.,[[.,.],[[.,.],.]]],[.,.]],.]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[[.,[[[.,.],.],[.,.]]],[.,.]],.]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[[.,[[.,.],[.,.]]],[[.,.],.]],.]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[[.,.],.],[.,[.,[[.,.],.]]]],.]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[[.,.],.],[.,[[.,[.,.]],.]]],.]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[[[.,.],.],[.,[[[.,.],.],.]]],.]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[[.,.],.],[.,[[.,.],[.,.]]]],.]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[[.,.],.],[[.,[.,[.,.]]],.]],.]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[[[.,.],.],[[.,[[.,.],.]],.]],.]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[[.,.],.],[[[.,[.,.]],.],.]],.]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[[[.,.],.],[[[.,.],[.,.]],.]],.]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[[[.,.],.],[[[.,.],.],[.,.]]],.]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[[[.,[.,.]],.],[.,[[.,.],.]]],.]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[[.,[.,.]],.]],.]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[[[.,[.,.]],.],[[[.,.],.],.]],.]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[[[.,[.,.]],.],[[.,.],[.,.]]],.]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[[[.,[.,[.,.]]],.],[[.,.],.]],.]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[[[.,[.,[[.,.],.]]],.],[.,.]],.]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[[[.,[[.,.],.]],.],[.,[.,.]]],.]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[[[.,[[.,.],.]],.],[[.,.],.]],.]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[[[.,[[.,[.,.]],.]],.],[.,.]],.]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[[[[.,[[[.,.],.],.]],.],[.,.]],.]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[[[.,[[.,.],[.,.]]],.],[.,.]],.]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[[[.,.],.],.],[[.,[.,.]],.]],.]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[[[.,[.,.]],.],.],[[.,.],.]],.]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[[[[.,[.,[.,.]]],.],.],[.,.]],.]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[[[.,[[.,.],.]],.],.],[.,.]],.]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[[[[.,.],[[.,.],.]],.],[.,.]],.]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],.]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[[.,.],[.,[[.,.],.]]],[.,.]],.]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[[[.,.],[[[.,.],.],.]],[.,.]],.]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[[.,.],.]],[.,.]],.]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],.]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],.]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[.,.],[.,[[.,[[[.,.],.],.]],.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[[.,.],[.,[[[.,[[.,.],.]],.],.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[[.,.],[.,[[[[.,[.,.]],.],.],.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,.],[.,[[[[.,.],[.,.]],.],.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,.],[.,[[[[.,.],.],[.,.]],.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[[.,.],[[.,[.,[[[.,.],.],.]]],.]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[[.,.],[[.,[[[.,[.,.]],.],.]],.]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,.],[[.,[[[[.,.],.],.],.]],.]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,.],[[.,[[[.,.],[.,.]],.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,.],[[.,[[[.,.],.],[.,.]]],.]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[[.,.],[[[.,[.,[[.,.],.]]],.],.]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[[.,.],[[[.,[[.,[.,.]],.]],.],.]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[[.,.],[[[.,[[[.,.],.],.]],.],.]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,.],[[[.,[[.,.],[.,.]]],.],.]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,.],[[[[.,[[.,.],.]],.],.],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,.],[[[[[.,[.,.]],.],.],.],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[[.,.],[.,.]],.],.],.]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,.],[[[[.,.],[.,[.,.]]],.],.]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,.],[[[.,.],[.,[[.,.],.]]],.]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[[.,[[.,.],.]],[.,.]],.]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[.,.],[[[[.,[.,.]],.],[.,.]],.]]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[[.,.],[[[[[.,.],.],.],[.,.]],.]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,[[[.,.],.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[[.,.],[[[.,[[.,.],.]],.],[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[[.,[.,.]],[[[.,[[.,.],.]],.],.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[[[.,.],.],[.,.]],.]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[[.,[.,[[[[.,.],.],.],.]]],[.,.]]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[[.,[[.,.],.]],[[[.,[.,.]],.],.]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[[.,[[.,[[[.,.],.],.]],.]],[.,.]]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],.],.]],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],.],.]],[[.,.],.]]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[[.,[[[.,[[.,.],.]],.],.]],[.,.]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[[.,[[[[.,.],.],.],.]],[[.,.],.]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[[.,[[[[.,[.,.]],.],.],.]],[.,.]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[[.,[[[[[.,.],.],.],.],.]],[.,.]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[[.,[[[[.,.],[.,.]],.],.]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[[.,[[[[.,.],.],[.,.]],.]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],.]],[[.,.],.]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[[.,[[.,.],[[[.,.],.],.]]],[.,.]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[[.,[[[.,.],.],[[.,.],.]]],[.,.]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[[.,[[[[.,.],.],.],[.,.]]],[.,.]]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],.],[.,[[.,[[.,.],.]],.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,.],.],[.,[[[.,[.,.]],.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,.],.],[[.,[.,[[.,.],.]]],.]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,.],.],[[.,[[.,[.,.]],.]],.]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[[.,.],.],[[.,[[[.,.],.],.]],.]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[[[.,.],.],[[[.,[.,[.,.]]],.],.]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],.],[[[.,[[.,.],.]],.],.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],.],[[[[.,[.,.]],.],.],.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[[[.,.],.],[[[[.,.],[.,.]],.],.]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[[[.,.],.],[[[.,[.,.]],[.,.]],.]]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],.],[[.,.],[[.,[.,.]],.]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[[[.,[.,[[.,.],.]]],.],[[.,.],.]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[[[.,[.,[[[.,.],.],.]]],.],[.,.]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[[[.,[[.,.],.]],.],[.,[[.,.],.]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[[[.,[[.,.],.]],.],[[.,[.,.]],.]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[[[.,[[.,.],.]],.],[[.,.],[.,.]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],.],[[.,.],.]]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[[[.,[[.,[.,[.,.]]],.]],.],[.,.]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[[[.,[[.,[[.,.],.]],.]],.],[.,.]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,[[[.,.],.],.]],.],[[.,.],.]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[[[.,[[[.,[.,.]],.],.]],.],[.,.]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[[[.,[[[[.,.],.],.],.]],.],[.,.]]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[[[.,[[[.,.],[.,.]],.]],.],[.,.]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[[[.,[[.,.],[[.,.],.]]],.],[.,.]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[[[.,[[[.,.],.],[.,.]]],.],[.,.]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[[[.,[[.,.],[.,.]]],.],[[.,.],.]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[[[[.,.],.],.],[[.,[.,[.,.]]],.]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[[[[.,.],.],.],[[[.,[.,.]],.],.]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[.,[.,.]],.],.],[[.,[.,.]],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[[[[.,[.,[[.,.],.]]],.],.],[.,.]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[[[[.,[[.,.],.]],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[[[[.,[[.,[.,.]],.]],.],.],[.,.]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[[[[.,[[.,.],[.,.]]],.],.],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[[[[.,.],[.,[[.,.],.]]],.],[.,.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[[[[.,.],[[.,[.,.]],.]],.],[.,.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[[[[.,.],[[[.,.],.],.]],.],[.,.]]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[[[[.,.],[[.,.],[.,.]]],.],[.,.]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[[.,.],.]],.],[.,.]]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[[[[.,[[.,.],.]],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[[[[.,.],[.,.]],.],[[.,[.,.]],.]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[[[.,.],.],.]]],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[[.,[.,.]],.],.]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[[[.,.],[[[.,.],[.,.]],.]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[[[[.,[[.,.],.]],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[[[.,.],.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[[[[.,.],.],[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[[[.,[.,.]],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[.,[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[[[.,.],[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[[[.,.],[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[.,[[[.,.],[[.,.],.]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[[[.,.],[.,.]],.]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,.]]],[[[[.,.],.],.],.]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[.,.],[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[.,[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[[[[.,.],.],.],.]]]
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,.]]],[[.,[[.,.],.]],.]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[[.,.],[.,.]],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[[.,[[.,.],.]],.]]]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[.,[[[.,.],.],.]]]]
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[[[.,.],[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[[[.,.],[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>[[[[.,.],.],[.,[.,.]]],[[[.,.],.],.]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[[[.,.],[.,[.,.]]],.],[[[.,.],.],.]]
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[.,[[[[.,.],[.,.]],.],[[[.,.],.],.]]]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[[[.,.],[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[.,.]],[[.,.],.]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],[.,.]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[[.,.],[.,.]],[[.,.],[.,[.,.]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[[[.,.],[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[.,[[[.,.],[.,.]],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[.,[[[[.,.],[.,.]],[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[[[.,.],[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,1,0]=>[[[[[.,.],.],.],[.,[.,.]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0]=>[[[[.,.],.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[[[[.,.],[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[.,[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[[.,.],.]]],[[[.,.],.],.]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[.,[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],[[[.,.],.],.]]],.]
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[.,[[[[.,.],[.,.]],[[[.,.],.],.]],.]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[[[.,.],[.,[.,[.,.]]]],[[[.,.],.],.]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,1,0]=>[[[[[.,.],.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[[[[[.,.],.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[.,[[[.,.],[.,[.,.]]],[[[.,.],.],.]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[[.,.],.]]],[[.,[.,.]],.]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[[.,.],.]]],[.,[[.,.],.]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[.,[[[[[.,.],.],.],[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],[[.,[.,.]],.]]],.]
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],[.,[[.,.],.]]]],.]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[[[.,.],[.,.]],[[[.,.],.],.]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0]=>[[[.,.],[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0]=>[[[.,.],[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[.,[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[.,[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0]=>[[[[.,.],.],[.,[[.,.],.]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[[.,.],.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[[[.,.],[.,[[.,.],.]]],.],[[.,.],.]]
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[.,[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]]
[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]
[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]=>[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[.,[[[.,.],[.,[.,.]]],[[.,.],.]]],.]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,[[[.,.],[.,.]],[[.,.],.]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[.,[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[.,[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[.,[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[.,[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[.,[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[.,[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[[[[.,.],.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[[[.,.],[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[[[.,.],[.,.]],[[[.,.],[[.,.],.]],.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]
[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]=>[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]
[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]=>[[[[[.,.],.],.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[[[.,.],[[.,.],.]],[[.,.],[.,.]]],.]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[[[.,.],.],[.,.]],[[.,.],[.,.]]],.]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[.,[[[.,.],.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[[[[.,.],.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[.,[[[.,.],[.,[[.,.],.]]],[[.,.],.]]]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[[.,[.,.]],[.,.]],[[[.,.],[.,.]],.]]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[[[.,.],[[.,.],.]],[[[.,.],[.,.]],.]]
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[[[.,[[.,.],.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.],.]
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[.,.],[[[.,.],[.,.]],[[[.,.],.],.]]]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[[[.,.],[.,.]],.]],.]
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,.],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[.,.],[[[.,.],[.,.]],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[[[.,[[.,.],[.,.]]],.],[[.,[.,.]],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[.,[[[.,.],[.,.]],[[.,.],.]]],.],.]
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[[.,[[[.,.],[.,.]],[.,[.,.]]]],.],.]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,[[[.,.],[[.,.],.]],[[.,.],.]]],.]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[[[[.,.],[.,.]],[[.,.],[[.,.],.]]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[[[[[.,[[[.,.],.],.]],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[.,[[[[[.,[[[.,.],.],.]],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[.,[[[[[.,[.,[[.,.],.]]],.],.],.],.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[.,.],[.,[[.,[[.,[.,.]],.]],.]]],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,.],[[.,.],[.,[[.,[.,.]],.]]]],.]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[.,.],.],[.,[[.,[[.,[.,.]],.]],.]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,.],.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[.,.]],.],[[.,[[.,[.,.]],.]],.]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],.]],[.,[[.,[.,.]],.]]],.]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],.]],.],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[[[[[.,.],[[[.,.],.],.]],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[[[[[.,[.,.]],[[.,.],.]],.],.],.],.]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[[[.,.],[[.,.],[[[.,.],.],.]]],.],.]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[[[.,.],[[.,[.,.]],[[.,.],.]]],.],.]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[[[.,.],[[[.,.],[[[.,.],.],.]],.]],.]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[[[.,[.,.]],[[.,.],[[[.,.],.],.]]],.]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[[[.,.],[[[.,[.,.]],[[.,.],.]],.]],.]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],[[.,.],.]]],.]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[.,.],[[[[[.,[.,[.,.]]],.],.],.],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[[.,[.,.]],.],.],.],.]],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[.,.]],[[[[[.,[.,.]],.],.],.],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,.],[[[[.,[.,[.,.]]],.],.],.]],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[[.,[.,.]],[[[[.,[.,[.,.]]],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[[[.,[.,.]],[.,.]],.],.],.],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[[[.,.],[.,.]],.],.],.],.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[.,[[[[[[.,.],[.,.]],.],.],.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[[[.,[.,.]],[.,.]],.],.],.]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[.,[[[[[.,[.,.]],[.,.]],.],.],.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,[[[.,.],.],[.,.]]]],[.,.]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[[[.,.],.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[[.,.],[.,.]],[[[[.,.],[.,.]],.],.]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0]=>[[[[.,.],.],[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[[.,.],.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[.,[[.,[[.,[[.,.],.]],.]],.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[[[.,.],[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[[[.,.],.],.]]],[[.,.],.]]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[[[.,.],[[[.,.],[.,.]],[[.,.],.]]],.]
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[.,[[[.,.],[.,.]],[[.,.],.]]]],.]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[[.,[[.,.],.]],[[.,[[.,[.,.]],.]],.]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,.],.]],[[.,[.,.]],.]]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[.,.],[[.,[[.,.],.]],[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[[[[.,.],.],[[[[[.,.],.],.],.],.]],.]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[[[[.,.],.],.],.],.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[[.,[[.,.],.]],[[[[[.,.],.],.],.],.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[[[.,.],[.,[[.,[.,.]],.]]],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[.,[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[.,[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[.,[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[.,[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[.,[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[[[[.,.],[.,.]],[[.,[.,.]],[.,.]]],.]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[[[.,[.,.]],[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[[[.,.],[.,.]],[[.,[[[.,.],.],.]],.]]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]=>[[[.,.],[.,.]],[[.,[[.,[.,.]],.]],.]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[[[[.,.],.],.],.]],.]
[1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,.],[.,[[[.,.],[.,.]],[.,.]]]],.]
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[.,[[[.,.],.],[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,.],.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0]=>[[[.,.],[[[.,.],.],[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[[[[.,[[.,[.,.]],.]],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[.,[[[.,.],[.,[[.,[[.,.],.]],.]]],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[.,[[[.,.],[[.,.],[.,[[.,.],.]]]],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[.,[[.,[[[.,.],[.,[[.,.],.]]],.]],.]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[.,.],[[[.,.],[.,[[.,[.,.]],.]]],.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[[.,.],[[[[[.,.],.],.],.],.]],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[[[.,.],[[[.,.],[[.,.],.]],.]],.],.]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[[.,.],[[.,.],.]],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[.,[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[.,[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[.,[.,[[[[.,.],.],[.,.]],.]]]],.]
[1,1,0,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]],.]
[1,0,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[.,[[.,[.,[[[[.,.],.],[.,.]],.]]],.]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[[.,[.,[[[[.,.],.],[.,.]],.]]],.],.]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[.,[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[[.,[.,[[.,[[.,.],.]],[.,.]]]],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],[[[[[.,.],.],.],.],.]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[[[[.,.],[[[[.,.],.],.],.]],[.,.]],.]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[[.,[[.,.],[[[[.,.],.],.],.]]],[.,.]]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],[.,.]]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],[.,.]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[.,[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[.,[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[.,[.,[.,[.,[[.,.],.]]]]],.],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[.,.],.],[[[[[.,.],[.,.]],.],.],.]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[[[.,[.,[.,[[[.,.],.],.]]]],.],[.,.]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[[[.,[.,[.,[[.,[.,.]],.]]]],.],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[.,.],.],[[[[.,[.,.]],[.,.]],.],.]]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[[[.,.],.],[[[[.,.],[[.,.],.]],.],.]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[.,[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[.,[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[.,[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[.,[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[.,[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[[[[.,.],.],[.,.]],[[[.,.],.],[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[[[.,.],[.,.]],[[.,[[.,.],.]],[.,.]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[[[.,[.,.]],[.,.]],[[[.,.],.],[.,.]]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0,0]=>[[[.,[[.,.],.]],[.,.]],[[[.,.],.],.]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0,0]=>[[[.,.],[.,.]],[[[[.,.],.],[.,.]],.]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0]=>[[[.,.],[[.,.],.]],[[[.,.],.],[.,.]]]
[1,1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0,0]=>[[[.,[[.,.],.]],[.,.]],[.,[[.,.],.]]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0,0]=>[[[.,[[.,.],.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[.,.],[[[[[[.,.],.],[.,.]],.],.],.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],.],[[[[.,[[.,.],.]],.],.],.]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[.,[[[[[.,.],[.,.]],.],.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,.],[[[[.,[[.,.],[.,.]]],.],.],.]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[.,[[[[[[.,.],.],[.,.]],.],.],.]],.]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[[[.,.],[.,.]],[[[[.,[.,.]],.],.],.]]
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[[[.,.],[.,.]],[[[.,[.,[.,.]]],.],.]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[[[[[.,.],.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[[[[[[.,.],.],.],[.,.]],[.,[.,.]]],.]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]],.]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]],.]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,[[[[[[.,.],[.,.]],.],.],.],.]],.]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[.,[[[[[.,[.,[.,.]]],.],.],.],.]],.]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]],.]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]],.]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[[[.,.],[[.,.],.]],[[[[.,.],.],.],.]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[.,[[[[[.,.],.],.],.],[.,[[.,.],.]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[[[.,.],.],.],.]]
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[.,[[.,.],[.,.]]],[[[[.,.],.],.],.]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[[[[[.,.],.],.],.],[.,[.,.]]]],.]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],[.,.]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[.,[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[.,[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]],.]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],[[.,.],[.,.]]],.],.]
[1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],[[[.,.],.],.]],.],.]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[[[[.,.],[[.,.],.]],[[[.,.],.],.]],.]
[1,1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],[.,[[.,.],.]]],.],.]
[1,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[[[[.,.],[.,.]],[[.,[.,.]],.]],.],.]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[[[[.,.],[[.,.],.]],[.,[[.,.],.]]],.]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[[[[.,.],[[.,.],.]],[[.,[.,.]],.]],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0]=>[[[.,.],[[[.,.],.],.]],[[[.,.],.],.]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]=>[[[.,.],[[[.,.],.],.]],[.,[[.,.],.]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0,0]=>[[[.,.],[[[.,.],.],.]],[[.,[.,.]],.]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]],.]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[.,[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[.,[.,[.,[[[.,[.,.]],.],.]]]],.],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[.,[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[[[[.,.],.],[[.,.],.]],[[.,.],[.,.]]]
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[[[[.,.],[.,[.,.]]],[[.,.],[.,.]]],.]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,.],[.,[[[.,.],[.,[.,.]]],.]]],.]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[[[.,.],[[[.,[.,.]],.],[.,[.,.]]]],.]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[[[[[.,.],[[.,.],[.,.]]],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[[[[.,[[.,.],.]],[.,.]],.],.],.],.]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]],.]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[.,[[[.,.],[.,[[.,.],.]]],[.,.]]],.]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[[[[[.,[.,.]],.],[.,.]],.],.],.],.]
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0]=>[[[.,.],[[[.,.],.],[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[.,[[[.,.],[[[.,.],.],[.,.]]],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[.,[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[.,[[.,[[.,[[.,.],.]],.]],.]]],.]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[.,[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[.,.]],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],.],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,.]],.],[.,[[.,[[.,.],.]],.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],[.,[[.,[[.,.],.]],.]]],.],.]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[.,[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[.,[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],[.,[[.,[.,.]],[.,.]]]],[.,.]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[.,.],[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[[[.,.],.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[[[.,[[.,.],[.,.]]],[.,.]],[[.,.],.]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],[.,.]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[.,[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[.,[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[.,[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[.,[[[.,.],[.,.]],[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],[.,.]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[[[[.,.],.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[.,[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[.,[.,.]],[.,[[.,[[.,[.,.]],.]],.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[.,[[.,[[.,.],.]],.]]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[.,[[.,[.,.]],.]],[.,[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[.,[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[[[[.,.],[[[[.,.],.],.],.]],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[[[[[.,.],.],[[[.,.],.],.]],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[[[[.,[.,.]],[[[.,.],.],.]],.],.],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[[[[.,.],[.,[.,[.,.]]]],.],.],.],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[.,[.,[.,[[[[[.,.],[.,.]],.],.],.]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[[.,.],[.,.]]]],[[.,.],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,.],[.,.]]],[[.,.],.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[[[.,.],.],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[[[[.,.],.],[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],[.,.]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]],.]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[.,[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[.,[.,[.,[[[.,.],.],.]]]],.],.],.]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]],.]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.],.]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[.,[.,.]],[[[[[.,.],.],.],.],.]],.]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[[[[.,.],.],.],.]]]]],.]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[.,[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[.,[[[[[.,.],.],[.,[.,.]]],.],[.,.]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[.,[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[.,[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[.,[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[[[.,.],[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[[[.,.],[[.,.],.]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[[[.,.],.],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[[.,[[.,.],[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[[[[.,.],[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[[[.,.],.],[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[.,.],[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],.],[[[.,.],[.,.]],.]]
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[[.,[[.,.],.]],.]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,1,0,0]=>[[[[.,.],[.,[[.,.],.]]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[.,[[.,[.,[.,[[[[.,.],.],.],.]]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,[.,[.,[[[[.,.],.],.],.]]]],.],.]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[[[[[.,[.,.]],[.,[.,.]]],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[[[[[.,.],[[.,[.,.]],.]],.],.],.],.]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[.,[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[.,[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[.,[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]],.]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[.,[[.,.],[[[[[.,[.,.]],.],.],.],.]]]
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[[.,[[.,.],.]],.]],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]
[1,1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[[[.,.],.],.]],[.,.]]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[.,.],[.,[[[.,.],[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[.,[[[[.,.],[.,.]],.],[.,.]]]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[.,.],[.,[[[[.,.],.],[.,.]],[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[[[[[.,.],.],.],.],.]]]],.]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[.,[[.,[.,[[[[[.,.],.],.],.],.]]],.]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,[.,[[[[[.,.],.],.],.],.]]],.],.]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[.,.],[[[[[.,.],.],.],.],.]],.]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[.,[.,.]],[[[[[.,.],.],.],.],.]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[.,[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[.,[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[.,[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[.,[[[[[[.,.],[.,[.,.]]],.],.],.],.]]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[[[.,.],[.,[[.,.],.]]],[[.,.],[.,.]]]
[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[[[[[.,.],[.,.]],[.,.]],[[.,.],.]],.]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0,0]=>[[[[.,.],[[.,.],.]],[[.,.],.]],[.,.]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,.],.]],[[.,.],.]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[[[[.,.],[.,[[.,.],[.,.]]]],.],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[.,[[[.,.],.],[[.,[[.,[.,.]],.]],.]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[.,.],.],[[.,[[.,[.,[.,.]]],.]],.]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[.,[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[.,[.,.]],[[.,[[.,[.,[.,.]]],.]],.]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[.,[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[.,.],[[.,[[.,.],[[[.,.],.],.]]],.]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[.,.],[[.,.],[.,[[.,[.,[.,.]]],.]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[[.,.],[[.,[[.,.],.]],[.,.]]],.],.]
[1,0,1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[.,[.,[[.,[[[[.,.],.],[.,.]],.]],.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[.,.],[[.,[[.,.],.]],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[[.,[[[[.,.],.],[.,.]],.]],.]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[[[.,.],[[.,[[.,[.,.]],.]],[.,.]]],.]
[1,1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[.,[.,.]],[[.,[[.,.],.]],[.,.]]],.]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[.,[[[[.,.],.],[[.,.],.]],.]],.]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[.,[[[.,[[[[.,.],.],[.,.]],.]],.],.]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[[.,.],[.,.]],[[[[[.,.],.],.],.],.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0]=>[[[.,.],[.,.]],[[[[.,.],.],.],[.,.]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[[[.,.],[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0,1,0]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[[.,.],.],[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[[[[.,.],[.,.]],.],[[[.,.],.],[.,.]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0]=>[[[.,.],[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[[[[.,.],[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[.,[[[[.,.],.],[.,[.,.]]],[[.,.],.]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[.,[.,[[[[.,.],.],[.,.]],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[[[.,.],[[[.,.],.],.]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[[[[[[[.,.],.],.],[.,.]],.],.],[.,.]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[[[[[[[.,.],.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[[[[[[.,.],.],.],.],.],[[.,.],[.,.]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[[[[.,.],[[[.,.],.],.]],[[.,.],.]],.]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[[[[.,.],[[.,.],.]],[[.,.],.]],.],.]
[1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[[[.,.],[[.,.],.]],.],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[[[.,.],[.,.]],.],.],.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]=>[[[.,.],[[.,.],[.,.]]],[[[.,.],.],.]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0]=>[[[.,.],[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0]=>[[[.,.],[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]],.]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[.,[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]],.]
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0]=>[[[.,.],[.,.]],[[.,[.,[[.,.],.]]],.]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[[[[[.,.],.],[.,.]],.],[[[.,.],.],.]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[[[[[[.,.],.],.],.],[[.,.],.]],.],.]
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[[[.,.],[.,.]],.],[[[[.,.],.],.],.]]
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0]=>[[[.,.],[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0,0]=>[[[[.,.],.],[.,.]],[[.,[[.,.],.]],.]]
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[[[[.,.],.],.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[[[[.,.],.],[.,.]],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[[.,.],[[[.,.],.],.]],.],.],.]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[[.,[.,[.,[.,.]]]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[[[.,[[[.,.],.],.]],.],.],[.,.]],.]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0]=>[[[.,.],[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[.,[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,0]=>[[[.,.],[[[[.,.],.],.],[.,.]]],[.,.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[.,.],[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[.,.],[[[[[.,.],[.,.]],.],.],.]],.]
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]],.]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[.,[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],.],[[.,.],.]]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],[.,.]]
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[.,[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]]
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[.,[[.,.],[.,.]]],[[[.,.],[.,.]],.]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[[[[.,[.,[.,.]]],[.,.]],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.]
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],[.,.]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[.,[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[.,[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[[.,[[.,.],[.,.]]],[[[.,.],.],[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],.],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0]=>[[[[[.,.],[.,.]],.],[.,.]],[[.,.],.]]
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],[.,.]]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[[[.,.],[.,.]],[[[.,[[.,.],.]],.],.]]
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],.],.],[[[.,.],.],.]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[.,[[[.,.],[[.,.],.]],.]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,[.,.]],.]]
[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[[[[.,.],[.,.]],[[.,.],.]],.]]]
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],[.,.]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0]=>[[[[[[.,.],.],.],.],[.,.]],[[.,.],.]]
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0]=>[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,1,0]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[.,.],[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[.,[.,[[[[[.,.],.],.],.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,.]]]],[[[[.,.],.],.],.]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[.,[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[[[[[.,.],.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[.,[[[.,.],.],[.,.]]],[.,[.,.]]],.]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[[[.,[.,.]],.],.],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[[.,[[[.,.],.],.]],.],.],[[.,.],.]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[.,[.,.]],[[[[.,[.,.]],.],.],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[[[.,[.,.]],[[[[.,.],[.,.]],.],.]],.]
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[.,[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],[.,.]]
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[[[[[.,[.,.]],[.,.]],[.,.]],.],.],.]
[1,1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[[[[.,.],[.,[.,.]]],.],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[.,.],[.,[.,[.,[[[.,[.,.]],.],.]]]]]
[1,0,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[.,[.,[[[[.,.],[.,.]],.],[[.,.],.]]]]
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[[[[[[.,.],[.,.]],.],.],.],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0]=>[[[[[.,.],.],[.,.]],[.,.]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,[.,.]]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[[.,.],.]],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],.],[[.,.],.]],[.,.]]
[1,1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],[[.,.],.]],.],[.,.]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],[.,.]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[.,[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[[[.,[.,.]],[.,.]],.],[[.,.],[.,.]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[[[[.,.],[[.,.],[.,.]]],[[.,.],.]],.]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[[[[.,.],[[[.,.],.],.]],[.,[.,.]]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,.],[[[[[.,[[.,.],.]],.],.],.],.]]
[1,1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0,0]=>[[[[[.,.],[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[[[[[[[.,.],.],[.,.]],.],.],.],[.,.]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[.,[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[[[[.,.],.],.],[.,.]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[[[[[.,.],.],[[[.,.],.],.]],[.,.]],.]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[[[[.,[.,.]],[[[.,.],.],.]],[.,.]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[.,.],[[[[[.,.],[[.,.],.]],.],.],.]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[.,[[[[[.,.],.],.],.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],[.,.]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0,0]=>[[[.,.],[[.,.],[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[.,.],[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[[[[[.,.],.],[[.,.],[.,.]]],.],[.,.]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]]
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[[[.,[.,.]],.],.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[.,.],[[[.,.],.],[[[[.,.],.],.],.]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[[.,[.,.]],.],.]]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[[[.,[.,.]],[.,.]],.],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[.,.],[[[[.,[.,.]],[.,.]],.],.]],.]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[[[[.,.],[.,[[.,.],.]]],[.,[.,.]]],.]
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0,0]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[[[.,.],[[[.,[.,.]],[.,.]],.]],.],.]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[.,[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[.,[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]],.]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[.,[[[[[.,[.,[.,[.,.]]]],.],.],.],.]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0]=>[[[.,.],[[.,.],.]],[[.,[.,.]],[.,.]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0,0]=>[[[.,.],[[.,.],[.,.]]],[.,[[.,.],.]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,[.,.]]]],.],[[.,.],.]]
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[[[[[[.,.],[.,.]],.],.],.],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[.,[[[.,.],[.,.]],.]],[.,[.,.]]],.]
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],.],.],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],.]],[[.,.],[.,.]]]
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,0]=>[[[.,.],[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,0]=>[[[.,.],[.,.]],[[[.,[.,.]],.],[.,.]]]
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[[[.,.],[[.,.],.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[[[[[[.,.],.],.],.],[[[.,.],.],.]],.]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[[[.,.],[[.,[.,.]],.]],[[.,.],[.,.]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[.,[[[[.,.],[.,[.,.]]],.],[[.,.],.]]]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[[[.,.],[.,.]],.],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[[.,[[[.,.],.],.]],[.,.]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[[[[.,.],.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[[.,[.,[.,[[.,.],.]]]],[.,.]],.],.]
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0]=>[[[[[.,.],.],[.,.]],[[.,.],.]],[.,.]]
[1,1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[.,.],[[[[.,.],[.,.]],.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[.,.],[[[[.,.],[[[.,.],.],.]],.],.]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[[[[.,.],[[[.,.],[.,.]],.]],.],.],.]
[1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[.,.],[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[.,[[.,.],[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[[[.,[.,[.,[.,.]]]],.],[[[.,.],.],.]]
[1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[[[[.,.],[.,.]],.],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[.,[[.,.],[.,.]]],[.,[[[.,.],.],.]]]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[.,.],[[[[.,[.,[.,.]]],[.,.]],.],.]]
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0]=>[[[[[[.,.],[.,.]],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0,0]=>[[[[[[.,.],.],[.,.]],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0,0]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[[[[.,.],[[.,.],.]],[.,[.,.]]],.],.]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[[[[.,.],.],[[.,.],.]],[.,.]],.],.]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[[[[[.,.],[[.,.],.]],.],[.,.]],.],.]
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[[[[.,.],.],[.,.]],[[[[.,.],.],.],.]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0]=>[[[[[.,.],.],.],[.,.]],[[[.,.],.],.]]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[[[.,[.,[.,[.,.]]]],[.,.]],.]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0,0]=>[[[[[.,.],.],.],[.,.]],[.,[[.,.],.]]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[[[[[[.,.],.],.],[.,.]],.],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[[[[[.,.],[[[.,.],.],.]],.],[.,.]],.]
[1,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[[[[.,.],.],[[[.,.],[.,.]],[.,.]]],.]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0,0]=>[[[[.,.],[[.,.],.]],[.,.]],[[.,.],.]]
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[[[[[.,.],[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[.,.],[[[[.,.],.],[.,.]],[[.,.],.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[[.,.],.]],.],[.,[.,.]]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[.,[[[.,.],[[.,.],.]],[.,[.,.]]]],.]
[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[[[[[[.,.],.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0,0]=>[[[[[.,.],.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[[[[[[.,.],.],[.,.]],.],.],[[.,.],.]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[[[[.,.],.],[.,.]],[[[.,[.,.]],.],.]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[[[[[[.,.],.],[.,.]],[.,.]],.],[.,.]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0,0]=>[[[[[[.,.],.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0]=>[[[[.,.],.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[[[.,.],[[[[.,.],[.,.]],.],.]],.],.]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[[.,[[.,.],[[.,.],.]]],[.,.]],.],.]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[[[[.,[.,.]],[[.,.],.]],[.,.]],.],.]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[[[.,[[.,.],[[[.,.],.],.]]],[.,.]],.]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[[[[[.,[.,.]],[.,.]],.],[.,[.,.]]],.]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[[[[[.,[.,.]],.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[.,.],[[[[.,.],.],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[.,.],[[[[[.,.],.],[.,.]],.],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[.,.],[[[.,[.,.]],[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],[.,.]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[[.,[.,[[.,.],.]]],[[[[.,.],.],.],.]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[[.,[.,[[.,[.,[.,[.,.]]]],.]]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[.,[[[.,.],.],.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[.,[[[.,.],.],[[.,.],.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[[.,[[.,.],[[.,.],[.,.]]]],[[.,.],.]]
[1,1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[[.,[[.,.],[.,.]]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[[.,[[.,.],[.,.]]],[[[.,[.,.]],.],.]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[[[.,.],.],[[[.,.],[[.,.],.]],[.,.]]]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],[.,.]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[[[[.,.],.],.],[[[[.,.],.],.],[.,.]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[1,1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[[[[[[.,.],[.,.]],[.,.]],.],.],[.,.]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[[[[[[.,.],.],[.,.]],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],.],.],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[[[[[.,.],[.,.]],.],.],[[.,[.,.]],.]]
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[[[[[[.,.],[.,.]],.],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],[.,.]]
[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[[[[[.,.],[.,.]],[.,.]],.],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[.,.],[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[[[[.,.],[.,.]],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[[[[[.,.],.],[.,.]],.],[.,[[.,.],.]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[[[[.,.],[[.,.],[.,.]]],.],[[.,.],.]]
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[[[[[.,.],[.,.]],[.,.]],.],[[.,.],.]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[[[[[.,.],.],[.,.]],.],[[.,[.,.]],.]]
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[[[[.,.],[.,.]],.],[[.,[.,[.,.]]],.]]
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[[[[.,.],[.,.]],.],[[.,[[.,.],.]],.]]
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[[[[.,.],[.,.]],.],[[[.,[.,.]],.],.]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,0]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0,0]=>[[[.,.],[[.,.],.]],[.,[.,[[.,.],.]]]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0,0]=>[[[[.,.],.],[.,.]],[.,[.,[[.,.],.]]]]
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0,0]=>[[[[.,.],.],[.,.]],[.,[[.,[.,.]],.]]]
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0]=>[[[[.,.],.],[.,.]],[.,[[[.,.],.],.]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,0]=>[[[[.,.],.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]=>[[[[[.,.],.],.],[.,.]],[[.,[.,.]],.]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0]=>[[[[.,.],.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[.,[[.,.],.]],.]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[.,[[[.,[.,[[[.,[.,.]],.],.]]],.],.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[[[[.,.],[.,.]],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[[[[[.,.],.],.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[.,[[[[[.,.],.],.],[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[[[[.,[.,.]],.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[[[.,[[.,.],.]],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[.,[[[[.,[.,.]],.],[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[.,[[[.,[[.,.],.]],[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]=>[[[[.,.],.],[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[[[.,.],.],[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[.,[[[[.,.],.],[[.,.],.]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[.,[[[.,[.,[.,.]]],[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[.,[[[[.,.],.],[.,.]],[[[.,.],[.,.]],.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0]=>[[[[.,.],.],[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[[[.,[.,.]],[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[.,[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[.,[[[.,[.,.]],[.,.]],[[[.,.],[.,.]],.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]=>[[[[.,.],.],[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[.,[[[.,.],[.,[[.,.],.]]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,1,0]=>[[[.,.],[[.,.],.]],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,.]]],[.,[[[[.,.],.],.],.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[[[[.,.],.],[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[.,[[[[.,.],.],[.,.]],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[[[[.,[.,.]],.],.],.]]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[.,[[[[.,.],.],[.,.]],[[.,.],[.,.]]]],.]
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[[[[[.,.],.],[.,.]],[[.,.],[.,.]]],.]]
[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]=>[[[.,[.,.]],[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]]
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[[[.,[.,[.,.]]],.],.]]]
[1,0,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[.,[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]],.]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[[[[.,.],.],[.,.]],[[.,.],[.,.]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[[.,[[[.,.],[.,.]],.]],[.,[.,.]]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,[[[.,[[[.,.],.],.]],[.,.]],.]],.],.]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,[.,.]],[.,[[[.,[.,.]],[.,.]],.]]],.]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[.,[[[.,.],.],.]],[.,[[[.,.],.],.]]],.]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[.,[.,.]],[.,[[[.,.],.],.]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[[[[.,[.,.]],.],.],[.,[[[.,.],.],.]]],.]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[[.,.],.],.]],[[.,[[[.,.],.],.]],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[[.,[.,.]],.],.],[[.,[[[.,.],.],.]],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[.,[.,.]],[[.,[[[.,.],.],.]],[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[[.,.],.],.]],[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]],.],.]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[.,[[[[[.,[[[.,.],.],.]],.],.],[.,.]],.]]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[.,[[[.,[[[.,.],.],[.,.]]],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[.,[[[[[.,[.,.]],[.,.]],.],[.,[.,.]]],.]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[.,[[[[[.,[.,.]],.],.],[.,.]],.]],.],.]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,[.,.]],[.,[[.,[.,.]],[[.,.],.]]]],.]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[[[.,.],[[.,.],.]],.]],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,[[.,[[[.,.],.],.]],[[.,.],.]]],.],.]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,[.,.]],[[.,.],.]]],.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[[[.,[.,.]],.],.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[.,[.,.]],[[[[.,[.,.]],.],.],[.,.]]]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[.,[[[[[.,[.,.]],.],[.,.]],[.,[.,.]]],.]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[[[.,[[[.,.],.],.]],.],.],[[.,.],.]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[[[.,.],.],[[.,.],.]]],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[[.,.],.]],.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[.,[[[[.,[.,.]],.],.],[[.,.],.]]],.],.]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],.],[[.,.],.]],[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[[[.,[[[.,.],[.,[.,.]]],.]],[.,[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[.,.]],[[.,[[[.,.],.],.]],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[[.,.],.],.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[[.,[.,.]],.],.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[[[[[.,[[[.,.],.],.]],.],.],[.,[.,.]]],.]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[[[.,[[[.,.],.],[.,[.,.]]]],[.,[.,.]]],.]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[[[[[.,[.,.]],[.,[.,.]]],.],[.,[.,.]]],.]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[.,.]],[[[[.,[.,.]],.],.],[.,[.,.]]]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[[[[[.,[.,.]],.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[[.,[[[.,.],.],.]],.],.],[[.,[.,.]],.]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],.],[[.,[.,.]],.]]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],.],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[[.,[.,.]],.]],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[[.,[[[.,.],[.,.]],.]],[.,[[.,.],.]]],.]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[[[.,[[[.,.],[.,.]],.]],[[[.,.],.],.]],.]
[1,1,0,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[[[.,[[.,.],[.,.]]],[.,[.,[[.,.],.]]]],.]
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[[.,[[.,.],[.,.]]],[.,[[[.,.],.],.]]],.]
[1,1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[[.,[[.,.],[.,.]]],[[[[.,.],.],.],.]],.]
[1,1,0,1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[[[[[.,.],[.,.]],.],.],[.,[[.,.],.]]],.]
[1,1,0,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[[[[[[.,.],[.,.]],.],.],[[[.,.],.],.]],.]
[1,1,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],.],[.,[.,[[.,.],.]]]],.]
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],.],[.,[[[.,.],.],.]]],.]
[1,1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],.],[[[[.,.],.],.],.]],.]
[1,1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,[.,[.,[[.,.],.]]]]],.]
[1,1,0,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,[.,[[[.,.],.],.]]]],.]
[1,1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,[[[[.,.],.],.],.]]],.]
[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[[[[[.,.],.],.],.],.]],.]
[1,1,1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[.,[.,[[[.,.],[.,.]],.]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[[.,[.,[[[.,.],[.,.]],.]]],[[[.,.],.],.]]
[1,1,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[.,[.,[[.,.],[.,.]]]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[.,[.,[[.,.],[.,.]]]],[[[[.,.],.],.],.]]
[1,1,1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[.,[[[[.,.],[.,.]],.],.]],[.,[[.,.],.]]]
[1,1,1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[[.,[[[[.,.],[.,.]],.],.]],[[[.,.],.],.]]
[1,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],.]],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],.]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],.]],[[[[.,.],.],.],.]]
[1,1,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[[.,[[.,.],[.,.]]],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[[.,[[.,.],[.,.]]],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[[.,[[.,.],[.,.]]],[.,[[[[.,.],.],.],.]]]
[1,1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[.,[[.,.],[.,.]]],[[[[[.,.],.],.],.],.]]
[1,1,1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[[[[[.,.],[.,.]],.],.],.],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[[[[[[.,.],[.,.]],.],.],.],[[[.,.],.],.]]
[1,1,1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],.],.],[.,[[[.,.],.],.]]]
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],.],.],[[[[.,.],.],.],.]]
[1,1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[[[[.,.],[.,.]],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[[[[.,.],[.,.]],.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[[[[.,.],[.,.]],.],[.,[[[[.,.],.],.],.]]]
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[[[.,.],[.,.]],.],[[[[[.,.],.],.],.],.]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[[[[.,.],.],.],.]]]]
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[[[[[.,.],.],.],.],.]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[[.,.],[.,.]],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[[.,[[.,[[[.,.],.],[.,.]]],.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[[.,[[[.,.],.],[.,[[.,.],.]]]],.]],.]
[1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[[.,[[[.,.],[.,.]],[[.,.],.]]],.]],.]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[[.,[[[.,.],.],[.,[[.,[[.,.],.]],.]]]],.]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[[[.,.],.],[.,[[[.,.],.],[.,.]]]]],.]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[.,[[[.,.],[.,[[.,.],.]]],[[.,.],.]]],.]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],.],[.,[[.,[[.,[[.,.],.]],.]],.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],.],[.,[[.,[[[.,.],.],[.,.]]],.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],.],[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[.,.],.],[.,[[[.,.],[.,.]],[[.,.],.]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],[.,[[.,[[.,.],.]],.]]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,[[[.,.],.],[.,.]]]],[[.,.],.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,.]],.],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],.],[[.,[[.,.],.]],.]]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[[.,[.,.]],.],[[.,[[.,.],.]],.]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],.],[[.,[[.,.],.]],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[.,[.,.]],.],[[.,[[.,.],.]],.]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],.],[[.,.],[[.,[[.,.],.]],.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[[[.,[.,.]],.],[[.,.],.]]],.]],.]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[[.,[.,.]],.],[[.,.],.]]],.]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[[.,[.,.]],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[[.,.],[[[.,[.,.]],.],[[.,.],.]]]],.]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,.],[[[.,[.,.]],.],[[.,.],.]]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],[[.,.],.]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[.,[[.,[.,.]],.]],.],[[.,.],.]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,[[[.,[[.,[.,.]],.]],.],[[.,.],.]]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[.,[[.,[.,.]],.]],.],[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,[[[.,[.,.]],.],[[.,.],.]]],.],[.,.]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[.,[.,.]],.],[[.,.],.]],[.,.]],[.,.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],.],[[.,.],.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],.],[[.,.],[[.,.],.]]]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,[.,.]],.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[[[[.,[.,.]],.],[[.,.],.]],[.,.]]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[[.,[.,.]],.],[[.,.],.]],[.,.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[.,[.,.]],.],[[.,.],[[.,.],.]]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[.,[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]],.]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[.,.],[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[[[.,.],.],[.,[[.,.],.]]],.]]],.]
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[.,.],[[[.,[[[.,.],.],[.,[.,.]]]],.],.]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,[[[[.,.],.],[.,[[.,.],.]]],.]],.],.]
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[.,[.,.]],[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[[[.,.],.],[.,[.,.]]]]],.]
[1,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[.,.],[.,[.,[[[[.,.],.],[[.,.],.]],.]]]]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],[[[[.,.],.],[.,[[.,.],.]]],.]],.]
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[.,.],[[[.,[[[.,.],.],[[.,.],.]]],.],.]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[.,[.,[[[.,.],.],[[.,.],.]]]]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,[.,.]],[[[.,.],.],[.,[[.,.],.]]]],.]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[.,.],[[.,[[[.,.],.],[[[.,.],.],.]]],.]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,.],.],[.,[.,[[.,[.,.]],.]]]],[.,.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0]=>[[[[[.,.],.],[.,[[.,[.,.]],.]]],[.,.]],.]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[[[[.,.],.],[.,[.,[[[.,.],.],.]]]],[.,.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0]=>[[[[[.,.],.],[[.,[[.,.],.]],.]],[.,.]],.]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[[[.,.],.],[[.,[[[.,.],.],.]],.]],[.,.]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[.,[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]],.]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[[.,[[[.,[.,[[.,.],.]]],.],[.,.]]],.],.]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[[.,.],.],[[[.,.],[.,.]],.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0,1,0]=>[[[[.,[[.,[.,.]],.]],[.,[.,.]]],.],[.,.]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[.,.],[[[.,[[.,.],.]],[[.,.],[.,.]]],.]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[.,[.,[.,.]]],.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[[.,.],.]],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[.,[.,[[[[.,[[.,.],.]],.],.],[.,.]]]],.]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[.,[[[[.,[[.,.],.]],.],.],[.,.]]],.],.]
[1,1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[[[.,[.,[[[.,.],.],.]]],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[[[[.,.],.],.],[[[[.,.],.],[[.,.],.]],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[[.,[[[.,.],.],.]],[[[.,.],.],[[.,.],.]]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0,1,0]=>[[[[[.,[[.,.],.]],.],[.,[.,.]]],.],[.,.]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[[.,.],.],[[[.,[[.,[.,.]],.]],[.,.]],.]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[[.,[[.,[.,[[.,.],.]]],.]],[[.,.],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[[[.,[.,[.,.]]],.],[[[.,[.,.]],.],[.,.]]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[[[[.,[[[.,.],.],.]],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[[.,.],.],.],[[[[.,[.,.]],.],[.,.]],.]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[[.,[[[.,[[.,.],.]],.],.]],[[.,.],[.,.]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[[[.,[.,.]],.],[[[.,[.,[.,.]]],.],[.,.]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[[[[.,[[.,.],.]],.],.],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[.,[.,[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[.,[[.,[[.,.],[.,[[[.,.],.],[.,.]]]]],.]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[.,[.,[[[.,.],.],[.,[[[.,.],.],[.,.]]]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[.,[[.,[[[.,.],.],[.,[[.,.],[.,.]]]]],.]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[.,[.,[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[.,[[.,.],[.,[[.,[[[.,.],.],[.,.]]],.]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[.,[[.,.],[.,[[.,.],[.,[[.,.],[.,.]]]]]]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[.,[[.,[[[.,.],[.,[[.,.],.]]],[.,.]]],.]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[.,[[.,.],[.,[[[.,.],.],[.,[[.,.],.]]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[.,[[.,[.,[[.,[[[.,.],.],[.,.]]],.]]],.]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[.,[[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]],.]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[.,[[.,[.,[[[.,.],.],[.,[[.,.],.]]]]],.]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[[.,[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]],.]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]],.]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[.,[[.,[[[.,.],.],[.,[.,[[.,.],.]]]]],.]]
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[.,[[.,.],[.,[[[.,.],[.,[.,.]]],[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[.,[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]],.]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[.,[[.,.],[.,[[.,.],[.,[.,[[.,.],.]]]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[.,[[[.,.],.],[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[[.,[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[.,[[[.,.],[.,[[.,.],[.,[.,.]]]]],[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[.,.],[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[.,.],[.,[[.,[[.,.],[.,[[.,.],.]]]],.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[.,.],[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[.,.],[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[.,[[[.,.],.],[.,[[.,[.,[[.,.],.]]],.]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[[.,[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]],.]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[.,.],[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[[[.,[[[[.,.],[.,.]],[.,.]],.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[[[.,[[[.,[[.,.],.]],[.,.]],.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[[[.,[[.,[[[.,.],[.,.]],.]],.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[[[.,[[[.,.],[[.,.],[.,.]]],.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[[[.,[[.,[[.,.],.]],.]],[[.,.],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[[[.,[[.,.],.]],[[.,[[.,.],.]],[.,.]]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[[.,.],[[.,[[[.,.],[.,.]],.]],[.,.]]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[[.,.],[[.,[[.,[[.,.],.]],.]],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[[[.,[[.,.],.]],[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[[.,.],[[.,[[.,.],.]],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[.,.],[[.,.],[[.,[[.,.],.]],[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[[[.,[[[.,.],[.,[[.,.],.]]],.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[[[.,[[.,[[.,.],.]],.]],[.,[[.,.],.]]],.]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[[.,.],[.,[[.,.],.]]]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],[[.,[[.,.],.]],[.,[[.,.],.]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],[[.,.],[.,[[.,.],.]]]]],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[[[.,[[.,.],.]],[.,[[[.,.],[.,.]],.]]],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[[.,.],[.,[[[.,.],[.,.]],.]]]],.]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[[.,.],[.,[[[.,[[.,.],.]],[.,.]],.]]],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[.,[[[.,[[[.,.],[.,.]],.]],[.,.]],.]],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[.,[[[.,[[.,[[.,.],.]],.]],[.,.]],.]],.]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[[.,.],[.,[[[.,.],[[.,.],[.,.]]],.]]],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[.,[[[.,[[.,.],.]],[[.,.],[.,.]]],.]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[.,[[[.,.],[[.,[[.,.],.]],[.,.]]],.]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,[[[.,.],[[.,.],[[.,.],[.,.]]]],.]],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[.,[[.,[[.,.],.]],.]]],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],[[.,.],[.,[[.,[[.,.],.]],.]]]],.]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[[[.,.],[.,[[.,.],.]]],.]]],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[[[.,[[.,.],.]],[.,[[.,.],.]]],.]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[.,.],[[.,.],[.,[[.,.],.]]]],.]],.]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[.,[[.,[[[.,.],[.,.]],.]],.]]],.]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[[[.,.],[.,[[[.,.],[.,.]],.]]],.]],.]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[[.,[[[.,[[.,.],.]],[.,.]],.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[[.,[[[.,.],[[.,.],[.,.]]],.]],.]],.]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],[.,[[.,[[.,[[.,.],.]],.]],.]]],.]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[.,[[[.,.],[.,[[.,[[.,.],.]],.]]],.]],.]
[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]=>[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[.,[.,[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[.,[.,[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[.,[.,[.,[[[.,[[[.,[.,.]],.],.]],.],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[.,[.,[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[.,[.,[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[.,[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[.,[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[.,[.,[[[.,[[[.,[.,[.,.]]],.],.]],.],.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[.,[.,[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[.,[.,[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[.,[[[.,[[[.,[.,[.,[.,.]]]],.],.]],.],.]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[.,[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[.,[[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[.,[[.,[[.,[[.,[[[.,.],.],.]],.]],.]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,[.,.]],[[.,.],.]]],.]],.]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[.,[[.,[[.,[.,.]],[.,[[[.,.],.],.]]]],.]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,[[[.,.],.],.]],[[.,.],.]]],.]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,[.,.]],.],.],[[.,.],.]]],.]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[.,[[.,[.,.]],[.,[[.,[[[.,.],.],.]],.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[.,[[.,[.,.]],[.,[[.,[.,.]],[[.,.],.]]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[.,[[.,[[[.,.],.],.]],[.,[[[.,.],.],.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[.,[[[[.,[.,.]],.],.],[.,[[[.,.],.],.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[[.,[[.,[[[.,.],.],.]],.]],.]],.],.]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,[[.,[[.,[.,.]],[[.,.],.]]],.]],.],.]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,[[.,[.,.]],[.,[[[.,.],.],.]]]],.],.]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[.,[[.,[[[.,.],.],.]],.]]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[.,[[[.,.],[[.,.],.]],.]],[.,[.,.]]],.]
[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]=>[[[[[.,[.,.]],[[.,.],.]],.],[.,[.,.]]],.]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[.,[.,.]],.],[[.,.],.]],[.,[.,.]]],.]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[.,[[.,[[[.,.],.],.]],.]],.]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[[[.,.],.],.]],[[.,.],.]]]
[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]=>[[.,[[[.,.],.],.]],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[[.,[[[.,.],[[[.,.],.],.]],.]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]=>[[.,[[[.,.],.],[[[.,.],.],.]]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[[[[.,[.,.]],.],.],[[.,[.,.]],[[.,.],.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[[.,[[[.,.],.],.]],.],.],[[[.,.],.],.]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0]=>[[[[.,[.,.]],[[[.,.],.],.]],.],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[[[[.,[.,.]],.],[[[.,.],.],.]],[.,[.,.]]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[[[[[.,[.,[.,.]]],.],[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[[[.,[[[[.,.],.],.],[[.,.],.]]],.],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[[[[.,[[[.,[.,.]],.],.]],.],[.,.]],[.,.]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[[[.,[[.,[[[[.,.],.],.],.]],.]],.],[.,.]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[.,.],[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[[.,.],[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[.,[.,[[[.,.],.],[[.,.],.]]]],.],[.,.]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[[[[[.,[[.,[.,.]],.]],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[.,[[[.,[[[.,.],.],.]],.],.]],.],[.,.]]
[1,1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]]
[1,1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[[.,.],[[[[[.,[.,.]],[.,.]],.],.],[.,.]]]
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[.,[.,[[[[.,.],.],[.,.]],.]]],.],[.,.]]
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,.],[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[.,[.,.]],.],[[.,.],.]],[[.,.],.]],.]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0,0]=>[[[[.,[[.,[.,[.,.]]],.]],[.,.]],[.,.]],.]
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[[[[.,.],.],[[[[.,.],.],.],[[.,.],.]]],.]
[1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[[[[.,[.,[[.,[.,.]],.]]],[.,.]],[.,.]],.]
[1,1,0,1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[[.,.],.],[[.,[[[.,.],.],.]],[.,.]]],.]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],[[.,.],.]],[.,.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[[.,.],.],[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[[.,[.,.]],.],.],[[[.,.],.],[[.,.],.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0]=>[[[[.,[.,.]],.],[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,0,0]=>[[[[[.,[.,[[.,.],.]]],.],[.,.]],.],[.,.]]
[1,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[[.,[[.,[.,[[.,.],[[.,.],.]]]],.]],[.,.]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0,0]=>[[.,[[[[.,.],.],.],[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[[.,[[[.,[[.,.],.]],.],.]],.],.],[.,.]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[[.,[[.,[[[[.,.],[.,.]],.],.]],.]],[.,.]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],[[.,.],.]]],[[.,.],.]],.]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[[[.,[[.,.],[[.,[.,.]],[.,.]]]],[.,.]],.]
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[[[[[.,.],.],.],[[[.,.],.],[[.,.],.]]],.]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,0]=>[[[[.,[.,.]],[[.,.],[.,.]]],[.,[.,.]]],.]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[[[[[.,[.,[[.,.],.]]],[.,.]],.],[.,.]],.]
[1,1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[[.,[.,[[.,[[.,.],[[.,.],.]]],.]]],[.,.]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[[.,[.,[[[.,.],.],[[.,.],[.,.]]]]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[[[[[.,[[.,[[.,.],.]],.]],.],.],.],[.,.]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[[.,[[[.,[[[.,.],[.,.]],.]],.],.]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[[[.,[[[.,.],[[.,.],.]],.]],[[.,.],.]],.]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[[[.,[[.,.],[[.,.],[.,.]]]],[.,[.,.]]],.]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[[[[[[.,[[.,.],.]],[.,.]],.],.],[.,.]],.]
[1,1,1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[[.,[.,[[[[.,.],[.,.]],[.,.]],.]]],[.,.]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[.,[[.,[[[.,.],[.,[.,.]]],.]],[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[.,[.,[[.,[[[.,.],.],.]],[.,.]]]],.]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[[[[.,.],[[.,.],.]],.],[.,[.,.]]],.]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[.,[[[[.,.],[[.,[.,.]],.]],.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[[.,.],[[[[[.,.],.],.],[.,.]],.]],.]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[.,[[.,.],[[[[[.,.],.],.],[.,[.,.]]],.]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[.,[[[[[.,.],.],.],[.,[.,[[.,.],.]]]],.]]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[.,[[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]],.]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[.,[[.,[[.,[.,.]],[.,[.,.]]]],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[.,[[[[.,.],.],.],[.,[.,[[.,[.,.]],.]]]]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[[[.,.],.],.],[[.,.],.]]]],.]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[[.,.],.]],[.,[.,.]]],.]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[.,[[[.,[.,.]],[[.,[.,.]],.]],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[.,[[[.,[[.,[.,[[.,.],.]]],.]],[.,.]],.]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[.,[[.,[[.,[.,[[.,.],.]]],.]],[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[.,[.,[[.,.],[[[.,.],[.,.]],.]]]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[.,[[[[.,[.,[[.,.],.]]],.],[[.,.],.]],.]]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[.,[[[.,[.,[[.,.],.]]],.],[[.,[.,.]],.]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[.,[[[.,.],[.,[.,[[[.,.],[.,.]],.]]]],.]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[.,[[.,.],[.,[.,[[[.,.],[.,[.,.]]],.]]]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[.,.],.]],[[[.,.],[.,.]],.]],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[.,[[[.,[[[[.,.],.],[.,.]],.]],[.,.]],.]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[.,[[.,[[[[.,.],.],[.,[.,.]]],.]],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[.,[[.,[[.,.],.]],[[[.,.],[.,[.,.]]],.]]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]],.]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[[[[[.,.],.],[[.,.],.]],.],[.,.]],.]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[.,[[[[[.,.],.],[[.,[.,.]],.]],.],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[.,[[[.,.],[[.,[.,[[.,.],[.,.]]]],.]],.]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[.,[[.,.],[[.,[.,[[.,.],[.,[.,.]]]]],.]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[.,[[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]],.]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,.],[[[[.,[.,.]],.],[.,.]],.]],.]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[.,[[.,.],[[[[.,[.,.]],.],[.,[.,.]]],.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[.,.],.],[[[.,.],[[.,.],.]],.]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[.,[[[[.,[.,.]],.],[.,[.,[[.,.],.]]]],.]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[.,[[[.,[[[.,[.,.]],.],[.,.]]],[.,.]],.]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[.,[[.,[[[.,[.,.]],.],[.,[.,.]]]],[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[.,[[[.,.],.],[[[.,.],[[.,[.,.]],.]],.]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[.,[[[.,[.,.]],.],[.,[.,[[.,[.,.]],.]]]]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[.,[[[.,[.,.]],.],[[.,.],.]]]],.]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[[[.,[.,.]],.],[[.,.],.]],[.,.]],.]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[.,[[[[.,[.,.]],.],[[.,[.,.]],.]],[.,.]]]
[1,1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[[[[[[.,[[.,.],.]],.],.],[.,[.,.]]],.],.]
[1,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[[[[[.,.],.],[[[.,.],.],[[.,.],.]]],.],.]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[[[[[.,.],.],[[.,[.,.]],[.,[.,.]]]],.],.]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[[[[.,.],[[[[.,.],[[.,.],.]],.],.]],.],.]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[[.,.],[[[.,[.,[[.,.],.]]],.],.]],.],.]
[1,1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[[[[[[.,.],[[.,.],.]],[.,.]],[.,.]],.],.]
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[[.,[[[[.,.],.],[.,.]],.]],[.,.]],.],.]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[[[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]],.],.]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[[.,[.,[[[[.,.],[[.,.],.]],.],.]]],.],.]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[[.,[.,[[[.,[.,[[.,.],.]]],.],.]]],.],.]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[[[[.,[[.,[.,.]],[[.,.],.]]],[.,.]],.],.]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[[.,[.,[[[.,[[.,.],.]],.],[.,.]]]],.],.]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]],.],.]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]],.],.]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[.,[.,.]],.],[[.,.],.]],.],[[.,.],.]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0,0,0]=>[[[[[[.,[[.,.],.]],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0]=>[[[[[.,.],.],[.,[.,[[.,.],.]]]],.],[.,.]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[[[.,[[[[.,.],.],.],.]],.],[[.,.],[.,.]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[[[.,[[[.,.],.],.]],.],[[[.,[.,.]],.],.]]
[1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0,0,0]=>[[[[[.,.],.],[.,.]],.],[.,[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[[[.,[[.,.],[.,.]]],.],[[.,[[.,.],.]],.]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.],[.,.]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[.,.],[.,[.,[[[[.,.],[[.,.],.]],.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[.,.],[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],[[.,.],.]]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[.,.],[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[.,.],[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[.,.],[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0,0]=>[[[.,[[.,.],.]],[.,.]],[[.,[[.,.],.]],.]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[[[[[.,.],[.,.]],[.,.]],[[.,.],.]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[.,[.,[[.,.],.]]]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[.,[.,.]],[[[[.,.],.],.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[.,[.,.]],[[[.,.],.],[[[.,[.,.]],.],.]]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[[[[.,[[.,.],.]],[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[.,[.,.]],[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,1,0,0,0]=>[[[.,.],[[.,.],[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[[.,[.,[[[[.,[.,.]],.],[.,.]],.]]],[.,.]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[.,[[.,[.,.]],.]]],[[[.,[.,.]],.],.]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]],[.,.]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[[.,[[[.,.],[[.,[.,.]],[.,.]]],.]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[[.,[[[.,.],[[.,[.,[.,.]]],.]],.]],[.,.]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[[[[[.,[[[.,.],.],.]],[.,.]],.],[.,.]],.]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[[[[[.,[.,.]],[.,[.,[.,.]]]],.],[.,.]],.]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[.,[[[[.,[.,.]],[[.,[.,.]],.]],.],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[.,[.,.]],[[.,.],[.,[[[.,[.,.]],.],.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[.,[.,.]],[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,1,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[[[.,[[[.,.],[.,.]],[.,[.,.]]]],[.,.]],.]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[[[.,[[[.,.],.],[.,[.,[.,.]]]]],[.,.]],.]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[.,[[.,[[[.,.],.],[[.,[.,.]],.]]],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]],.],.]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[.,[[.,.],[[.,[[[.,.],.],.]],.]]],.],.]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[.,[[[[[.,[.,.]],.],[.,[.,.]]],[.,.]],.]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[.,[[[[.,[.,.]],.],[[.,.],.]],[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[[[[[.,.],.],.],[.,[[[.,[.,.]],.],.]]],.]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[[[[[.,.],.],.],[.,[.,[[[.,.],.],.]]]],.]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[.,[[[[.,.],.],.],[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[.,[[[[.,.],.],.],[[.,[[[.,.],.],.]],.]]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],.],[[.,.],.]],[[[.,.],.],.]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[[[.,[[[.,.],[.,[.,[.,.]]]],.]],[.,.]],.]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[.,[[.,[[[.,.],[[.,[.,.]],.]],.]],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[[.,[[[[[.,.],.],.],[.,[.,.]]],.]],.],.]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,[[[.,.],[.,[[[.,.],.],.]]],.]],.],.]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[.,[[[[[.,[.,.]],[.,[.,.]]],.],[.,.]],.]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[.,[.,[[[[.,[.,.]],[[.,.],.]],.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[.,[[.,[.,.]],[[[[.,.],.],.],[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[.,[[.,[.,.]],[[.,.],[.,[[[.,.],.],.]]]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[[.,.],.]],[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[[.,[.,[[[[.,.],.],.],[[.,.],.]]]],.],.]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]],.],.]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[.,[[[.,[[[.,.],.],[.,[.,.]]]],[.,.]],.]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[.,[.,[[.,[[[.,.],.],[[.,.],.]]],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,[[[[.,.],.],.],[[.,.],.]]],.],.]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[[.,[[.,.],[[.,[.,.]],[.,.]]]],.],.]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[[.,[[[.,.],.],[[.,.],.]]],.],.],[.,.]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[.,[.,[[[[[.,[.,.]],.],[.,.]],[.,.]],.]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[.,[.,.]],[[[[.,[.,.]],.],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[.,[[[[[[[.,.],.],[.,.]],.],.],[.,.]],.]]
[1,0,1,1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[.,[[.,[.,[[.,[[[.,.],.],.]],.]]],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[.,[[[[.,[.,.]],[.,.]],.],.]],[.,.]]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[.,[[[[[.,[[.,[.,.]],.]],.],.],.],[.,.]]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[[.,.],[[.,[[[.,.],.],.]],[.,.]]],.],.]
[1,1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[[[[[.,[.,[[.,[.,.]],.]]],.],[.,.]],.],.]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[[[.,[.,[[.,.],.]]],[[.,[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[[[.,[[[[.,.],[[.,.],.]],.],.]],[.,.]],.]
[1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[[[[[[.,[[.,.],.]],.],.],.],[[.,.],.]],.]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[[.,[.,[[.,[.,[[.,.],.]]],.]]],[[.,.],.]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[[.,[[[[.,.],.],.],.]],[[.,.],[[.,.],.]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[[.,[.,.]],.],.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[.,[[[.,[[[.,.],.],.]],[.,.]],.]],.]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]],.]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[.,.],[[[.,.],[[.,[.,.]],[.,.]]],.]]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[.,[[.,.],[[.,[.,[[.,.],.]]],[[.,.],.]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[.,[.,.]]],.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[.,[[[.,.],[.,[[[.,[.,.]],[.,.]],.]]],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[.,[[[.,[[.,.],.]],[.,[[[.,.],.],.]]],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[.,[[[.,[[[.,.],[.,[.,.]]],.]],[.,.]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[.,[[[[[.,[[.,.],.]],.],.],[.,[.,.]]],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[.,[[.,[.,.]],[[.,[[.,.],.]],[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[.,[[.,[[[.,.],.],.]],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[.,[[[[.,[.,.]],.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.],.]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[[.,[[.,.],[[[.,.],[[.,.],.]],.]]],.],.]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,[[[.,[[.,.],.]],[.,[.,.]]],.]],.],.]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]],.],.]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[[[.,.],[.,[.,.]]],.]]],.]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[[[.,.],.],.]],[.,[[.,[.,.]],.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[[[.,[.,.]],.],.],[.,[[.,[.,.]],.]]],.]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[.,[.,.]],[[.,[[[.,.],[.,[.,.]]],.]],.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[.,[.,.]],[[.,[.,.]],[.,[[.,[.,.]],.]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[[.,[[[.,.],.],.]],[[.,[[.,[.,.]],.]],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],.],.],[[.,[[.,[.,.]],.]],.]]
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[.,[.,[[[[[[.,.],.],[.,.]],.],[.,.]],.]]]
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[.,[.,[[[.,[[[.,[.,.]],.],[.,.]]],.],.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[[.,[[.,[[.,[.,.]],.]],[.,.]]],.],.]]
[1,0,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[.,[.,[[[.,[[.,.],[[.,.],.]]],[.,.]],.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[.,[.,[.,[[.,.],[[[.,.],.],[[.,.],.]]]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[[.,[[[[.,.],.],[[.,.],.]],.]],.],.]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[.,[.,[.,[[[.,.],.],[[.,.],[[.,.],.]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[.,[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]],.],.]
[1,1,0,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[[.,[.,[[[[.,.],.],[[.,.],.]],.]]],.],.]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[.,[[.,[[.,.],[[.,.],.]]],.]]],.],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],[.,[.,[[.,.],[[.,.],.]]]]],.]
[1,0,1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[.,[.,[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[.,[[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]],.]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[.,[[[.,[[.,[[.,.],[.,[.,.]]]],.]],.],.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,[[.,.],[[.,.],.]]]],.]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,[[[.,[[.,.],[.,[.,.]]]],.],.]],.],.]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[.,[[.,[[[.,.],.],.]],[.,[[.,[.,.]],.]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[.,[.,[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]],.],.]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[.,[.,[[[.,.],.],[[.,[[.,[.,.]],.]],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,[[[.,[[[.,.],.],.]],[.,.]],.]]],.]
[1,1,0,0,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[.,[.,[[[[[.,[.,.]],.],.],[.,.]],.]]],.]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]],.]
[1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[.,[[.,[[[.,.],.],.]],[[.,.],.]]]],.]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,[.,[[[[.,[.,.]],.],.],[[.,.],.]]]],.]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[[.,[[[.,[.,.]],[.,.]],.]],.],.]],.]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[[.,[[.,[.,.]],[[.,.],.]]],.],.]],.]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[[.,[.,.]],[.,[[[.,.],.],.]]],.]],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[[[.,[[[.,.],.],.]],[.,[.,.]]],.]],.]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[[[[[.,[.,.]],.],.],[.,[.,.]]],.]],.]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[.,.]],[[.,[[[.,.],.],.]],.]]],.]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]],.]
[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]=>[[.,[[[[.,[.,.]],.],.],[[.,[.,.]],.]]],.]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[.,[.,[[[.,[.,.]],[.,.]],.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[.,[[[.,[[[.,.],.],.]],.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[.,.]],[.,[[[.,[.,.]],[.,[.,.]]],.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[.,.]],[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[[.,[[[.,.],.],.]],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[[.,[[[.,.],.],.]],[.,[[[.,[.,.]],.],.]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[[.,[[[.,.],[.,[.,[.,.]]]],.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],.]],[[[.,[.,.]],.],.]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,1,0]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0]=>[[.,[[[.,.],.],[.,.]]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[[.,[[[.,.],.],[.,.]]],[[[.,[.,.]],.],.]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[[.,[.,.]],.],.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[[.,[.,.]],.],.],[.,[[[.,[.,.]],.],.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[[.,[[[.,.],.],.]],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[[.,[[[.,.],[.,.]],.]],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[[.,[[[.,.],.],[.,.]]],.],.],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[[[[.,[[[.,.],.],.]],[.,.]],.],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>[[[[.,[.,.]],[.,.]],.],[.,[[[.,.],.],.]]]
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[[[[.,[.,.]],[.,.]],.],[[[.,[.,.]],.],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[[.,[[[.,.],.],.]],.],[.,.]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0]=>[[[[.,[.,.]],.],[.,.]],[.,[[[.,.],.],.]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[[[[.,[.,.]],.],[.,.]],[[[.,[.,.]],.],.]]
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[.,[.,[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[[.,[[[.,.],.],.]],.],.],[.,.]]]]
[1,0,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[.,[.,[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[.,[.,[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[[.,[[.,[[[.,.],.],.]],[.,.]]],.],.]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[[.,[[[[.,[.,.]],.],.],[.,.]]],.],.]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[.,[[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[.,[[[.,[[[.,.],.],.]],[.,[[.,.],.]]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[.,[[[[[.,[.,.]],.],.],[.,[[.,.],.]]],.]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[.,[[.,[.,.]],[.,.]]],.]]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[.,[[.,[.,.]],[[.,[.,.]],[.,[[.,.],.]]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[.,[[.,[[[.,.],.],.]],[[.,[[.,.],.]],.]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[.,[[[[.,[.,.]],.],.],[[.,[[.,.],.]],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,[.,[[.,[[[.,.],.],.]],[.,.]]]],.],.]
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[[.,[.,[[[[.,[.,.]],.],.],[.,.]]]],.],.]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,[[[.,[[.,[.,.]],[.,.]]],.],.]],.],.]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,[[[.,[.,.]],[.,[[.,.],.]]],.]],.],.]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,[[.,[.,.]],[[.,[[.,.],.]],.]]],.],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,[.,.]],[.,[.,[[.,[.,.]],[.,.]]]]],.]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[[[.,[[.,.],.]],.],.]]],.]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[[[.,[[[.,.],.],.]],[.,[.,[[.,.],.]]]],.]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[[[[[.,[.,.]],.],.],[.,[.,[[.,.],.]]]],.]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[.,[.,.]],[[.,[.,[[.,[.,.]],[.,.]]]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[.,[.,.]],[[.,[[[.,[[.,.],.]],.],.]],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[[.,[[[.,.],.],.]],[[.,[.,[[.,.],.]]],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[[.,[.,.]],.],.],[[.,[.,[[.,.],.]]],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]
[1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.]
[1,1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]
[1,0,1,1,0,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]
[1,0,1,1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]
[1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]]
[1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],.],[[.,.],[[.,.],.]]],.]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[.,[[.,.],[[.,[[[.,.],[[.,.],.]],.]],.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[.,[[.,.],[[.,[[.,.],[[.,[.,.]],.]]],.]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[.,[[.,[[.,[.,.]],.]],[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[.,[[[.,[.,.]],.],[[.,[[.,[.,.]],.]],.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[.,[[[.,[.,.]],.],[[.,.],[[.,[.,.]],.]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.],.]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,[[[[.,[.,.]],.],[[.,.],.]],.]],.],.]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],[[.,[[.,[.,.]],.]],.]]],.],.]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]],.],.]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,[[[.,[.,.]],.],[[.,[.,.]],.]]],.],.]
[1,1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[[[.,[.,.]],[[.,[[.,[.,.]],.]],[.,.]]],.]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],[[[.,[.,.]],.],[[.,.],.]]],.]
[1,1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[[[.,[[[.,[[.,[.,.]],.]],.],.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[[[.,[[[[.,.],.],[.,.]],.]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[[[.,[[[.,[.,.]],.],[.,.]]],[.,[.,.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[[.,[[.,[.,.]],.]],.],.],[[.,.],.]],.]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[[[[.,[.,.]],.],[[[.,.],[[.,.],.]],.]],.]
[1,1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[[[[.,.],.],[[.,.],.]],.],[.,[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[.,.]],[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[.,[.,.]],[[.,.],[[.,[[.,[.,.]],.]],.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[.,.],[[.,[.,[[[.,.],[[.,.],.]],.]]],.]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[.,.],[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[[[.,[[.,[.,.]],.]],.],.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[[.,[[.,[.,.]],.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[[.,[[[[.,.],.],[.,[.,.]]],.]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[[.,[[[.,[.,.]],.],[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[[.,[[.,[.,.]],.]],.],.],[[.,[.,.]],.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[.,[.,.]],.],[[.,[.,[[.,[.,.]],.]]],.]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],.],[[[.,.],[[.,[.,.]],.]],.]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[[[[[.,.],.],[[.,[.,.]],.]],.],[.,[.,.]]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],.],[[.,.],.]],[.,[[.,.],.]]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0]=>[[[[[.,[.,.]],[[.,.],.]],[.,.]],.],[.,.]]
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[[.,[[.,[[[.,.],[[.,.],.]],.]],.]],[.,.]]
[1,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0]=>[[[[.,[.,[[.,.],.]]],[[.,.],.]],.],[.,.]]
[1,1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[.,.],[[[[.,[.,.]],[.,.]],.],[.,.]]],.]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[[.,.],.]],[[[.,[[.,.],.]],[.,.]],.]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0]=>[[[[.,[.,.]],[[[.,.],[.,.]],.]],.],[.,.]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[[.,[[.,[[.,.],.]],.]],[[[.,.],[.,.]],.]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[[.,[[[[.,[.,.]],[[.,.],.]],.],[.,.]]],.]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[[.,[[.,[[.,.],.]],[[[.,.],[.,.]],.]]],.]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[[.,.],[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[[.,.],[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[[[.,[[[.,.],[[.,[.,.]],.]],.]],.],[.,.]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[[[.,[[.,[[.,.],.]],.]],.],[[.,[.,.]],.]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[[.,.],[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[[.,.],[[[[.,.],[.,[.,.]]],.],[.,.]]],.]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[[[.,[[.,.],.]],.],[[[.,.],[.,[.,.]]],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]]
[1,0,1,1,0,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[.,[[[[.,[.,.]],[.,.]],.],[.,.]]],.]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[.,[[.,[[.,[[.,[[.,.],.]],.]],[.,.]]],.]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[[.,.],[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[[.,.],[.,[.,[[.,[[.,.],.]],[.,.]]]]],.]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[.,.],.]],.],[[.,[.,[[.,.],.]]],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[[.,.],[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[.,[[.,[[.,[[.,[[.,.],.]],[.,.]]],.]],.]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[.,[[.,[[.,[[.,.],.]],[.,[[.,.],.]]]],.]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]]
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[.,[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]]
[1,0,1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0,0]=>[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[.,[.,.]],[[.,[[.,[[.,.],[.,.]]],.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[[.,[[[.,.],[.,.]],[.,.]]],.]]
[1,1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]],.]
[1,1,0,0,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[[.,[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[.,[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[.,[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]],.]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[[.,[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]],.]
[1,1,0,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.]
[1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[[.,[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]],.]
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[[.,[[.,.],[.,.]]],.]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]
[1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0]=>[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[[.,[[.,.],[.,.]]],.]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[.,.]]
[1,1,1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[[.,[[.,.],[.,.]]],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[[[.,[[.,[[.,[.,.]],[.,.]]],.]],.],[.,.]]
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[[[.,[[[.,[.,.]],[.,.]],[.,.]]],.],[.,.]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[[[[.,[[.,[.,.]],[.,.]]],.],[.,.]],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[[[[[.,.],.],[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0]=>[[[[.,[.,.]],.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[.,[[[.,.],[.,.]],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[.,[.,[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[.,[[[.,.],[.,[.,[.,.]]]],[[[.,.],.],.]]]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[.,[.,[[[.,.],[.,[.,.]]],[[[.,.],.],.]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[[[[[.,.],.],.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],.]
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[[[.,[[[.,.],.],.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.],.]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[[[[[[.,.],.],.],[.,.]],[[.,.],[.,.]]],.]
[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[.,.],[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[.,[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],.],[[.,.],[.,[[.,[[.,.],.]],.]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[.,[.,[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[.,[.,[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,.],[[[[[[[.,[.,.]],.],.],.],.],.],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[.,.],[[[[[[.,[.,[.,.]]],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,.],[.,[[[.,.],[.,.]],[.,.]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[[[[[[.,.],.],.],.],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,[[[.,.],.],[.,.]]]],[.,[.,.]]]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[.,.],[[[[.,.],.],[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[.,[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[.,.],[[[[[[.,.],.],.],.],.],.]],.],.]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[.,[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[.,[.,[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[[[[[.,[.,.]],.],.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[1,1,0,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[.,[[[.,.],[.,[[[.,.],.],[.,.]]]],[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[.,[[[.,.],[.,[[.,[[.,[.,.]],.]],.]]],.]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[[[[[[.,.],[[[.,.],.],.]],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[.,[.,[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[.,[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],[.,.]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],[.,.]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[.,.],.],[[[[[[.,.],[.,.]],.],.],.],.]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[.,[.,[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[.,[.,[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[[[.,.],.],[.,.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0]=>[[[[.,.],.],[.,.]],[[.,[[.,.],.]],[.,.]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0]=>[[[[[.,.],.],.],[.,.]],[[[.,.],.],[.,.]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0,0]=>[[[.,[.,.]],[.,.]],[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[.,.],[[[[[[[.,.],.],[.,.]],.],.],.],.]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0,0]=>[[[.,[.,[.,.]]],[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0]=>[[[.,[.,.]],[[[.,.],.],.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]],.]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]],.]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]],.]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[[.,[.,[.,.]]],[.,.]],[[.,.],[.,.]]],.]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0]=>[[[.,[.,.]],[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[[[.,.],[.,[.,[.,.]]]],[.,[[[.,.],.],.]]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[.,[[[.,.],[.,[.,.]]],[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[[[[.,.],.],[.,.]],[[.,.],[.,.]]],.],.]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[[[[[.,.],.],[.,.]],[[.,.],[[.,.],.]]],.]
[1,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],.],.]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[[[[.,[.,.]],[.,.]],[[.,.],[[.,.],.]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[[[[.,.],.],[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[.,[[[.,.],[.,.]],[[.,.],[.,[[.,.],.]]]]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[.,[[[.,[.,.]],[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[[[[[[[.,.],[[.,.],.]],.],.],.],.],.],.]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[.,[[[.,.],[[.,.],.]],[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[.,[.,[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[[[[.,[[.,.],.]],.],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[.,[[[.,.],[[.,.],.]],[[.,.],[.,.]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,.]],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],.],[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],[[.,.],.]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[[.,.],.],[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[[[.,[.,[[.,.],.]]],[.,.]],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[.,[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[.,.],[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[.,.]],[.,[[.,[[.,[[.,.],.]],.]],.]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[[[[[.,.],[[[[.,.],.],.],.]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]],.]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[.,[[[.,.],[.,[.,.]]],[.,[[[.,.],.],.]]]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,[[.,.],.]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[.,[.,[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]=>[[[.,[[.,.],.]],[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[[[[[.,[.,.]],.],[.,.]],[[.,.],[.,.]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[[.,[[[.,.],.],[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[[[.,[[.,.],.]],[.,.]],[[[.,.],[.,.]],.]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[[[.,.],[.,.]],[[[.,.],[.,[[.,.],.]]],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[.,[.,[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[1,1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0,0]=>[[[.,.],[[.,[.,.]],[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,.],[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[.,.],[.,[[[.,.],[.,.]],[[[.,.],.],.]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],[[.,.],.]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[[[[.,.],.],[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[[[[.,.],.],[.,.]],[[[.,.],[[.,.],.]],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,.]],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[[.,.],[.,.]]]],[[[.,.],.],.]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[.,[.,.]],.],[[.,[[.,[.,[.,.]]],.]],.]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0,1,0]=>[.,[[[.,.],[[.,[[.,[.,.]],.]],.]],[.,.]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[.,.],[[.,[[.,[.,[.,.]]],.]],.]],[.,.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[.,[[.,[[.,[[[[.,.],.],[.,.]],.]],.]],.]]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[[[.,.],[[.,[[.,.],.]],[.,.]]],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[.,[.,[.,[[.,[[[[.,.],.],[.,.]],.]],.]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[.,[.,[.,[.,.]]]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[[[[.,.],[.,[.,.]]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[[[.,.],[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0,0]=>[[[[.,.],.],[.,.]],[[[[.,.],.],.],[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0,1,0]=>[[[.,.],[.,.]],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0,0]=>[[[[.,.],.],[[.,.],.]],[[[.,.],.],[.,.]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0,1,0]=>[[[.,.],[.,[.,.]]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0,1,0]=>[[[.,.],[.,.]],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[[[[.,[.,[.,.]]],.],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0,1,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],[[.,[.,.]],.]]
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],[[.,.],[.,.]]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,1,0,1,0]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0,1,0]=>[[[[.,.],.],[.,[.,[.,.]]]],[[[.,.],.],.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,.]]],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,1,0]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[.,[.,[[[.,.],[[.,.],.]],[[.,.],[.,.]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[[[[.,.],.],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[[[[.,.],[.,.]],[[.,.],[[[.,.],.],.]]],.]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[[[[[.,.],[.,.]],[[.,.],[[.,.],.]]],.],.]
[1,1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[[.,[[[.,[.,.]],.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[.,.]],[[[[[[.,[.,.]],.],.],.],.],.]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]],.]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,1,0]=>[[[.,.],[[.,.],.]],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[.,[[[.,.],[.,[.,.]]],[[[.,.],.],.]]],.]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[.,[[[.,.],[.,.]],[[[.,.],[.,[.,.]]],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],[.,.]]]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],[.,.]],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[.,[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[[[[.,.],.],[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[[[[.,.],[.,.]],.],.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]],.]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],[[.,.],.]]
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[[[[.,[[.,.],.]],[.,.]],[[.,.],[.,.]]],.]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]=>[[[[.,[.,.]],.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],.]],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[[.,[[[.,.],.],[[.,.],.]]],[[.,.],[.,.]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.]
[1,0,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[.,[.,[[[.,.],[.,.]],[[[.,.],[.,.]],.]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[.,[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[[[[[.,.],.],[[.,.],.]],[[.,.],[.,.]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[[[[.,[.,.]],[.,.]],.],.],.],.]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],[.,.]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[[[.,.],[.,.]],[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[.,[.,[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0]=>[[[.,[.,[.,.]]],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[[[[.,[.,.]],[.,.]],.],.],.]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[.,[[[.,.],[.,[[.,.],.]]],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[[[[[[.,[[[.,.],.],.]],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0]=>[[[[[.,.],.],.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]],.]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[[.,.],.]],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[.,.],[[[[[[.,.],[[.,.],.]],.],.],.],.]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0]=>[[[[.,[.,.]],.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[[[[[[.,[.,.]],.],[.,.]],.],.],.],.],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0]=>[.,[[[.,.],[.,[.,[.,.]]]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[.,.],[[[.,.],[.,.]],[[[.,.],[.,.]],.]]]
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[[[[[.,.],.],.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[.,[[.,[.,[.,.]]],[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[.,[[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[[.,[[[[.,.],.],.],[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[[[[[[.,.],[[.,.],[.,.]]],.],.],.],.],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]]
[1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[[[[[.,.],[[.,.],.]],[[[.,.],.],.]],.],.]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0]=>[[[[.,.],[[[.,.],.],.]],[[[.,.],.],.]],.]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[[.,[.,.]],.],.],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[[.,.],.],.]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]=>[[[[.,.],[[[.,.],.],.]],[.,[[.,.],.]]],.]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0,0]=>[[[.,.],[[.,.],[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0,0]=>[[[[.,.],.],[[.,.],.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[.,.],[[[[[[.,.],[.,.]],.],.],.],.]],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[[[[.,.],[.,.]],.],.],.],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[.,.],[[[[[.,[.,.]],[.,.]],.],.],.]],.]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],[.,.]]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[[.,.],[[[.,.],[.,.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],[.,.]]
[1,1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[[[[[.,.],[[.,.],.]],[.,[[.,.],.]]],.],.]
[1,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[[[[[.,.],[[.,.],.]],[[.,[.,.]],.]],.],.]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0,0]=>[[[[.,.],[[[.,.],.],.]],[[.,[.,.]],.]],.]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0,0]=>[[[.,[[.,.],.]],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]],.]
[1,1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[.,.],[[[.,.],[[.,.],.]],[[.,.],[.,.]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[[[.,.],[.,.]],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0,0]=>[[[.,.],[[.,.],.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]],.],.]
[1,1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[[.,[[.,[[.,.],.]],[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[[.,[[[.,.],.],[.,.]]],[[[.,.],[.,.]],.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[[[[.,.],[.,.]],[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[.,[[[[.,.],[.,.]],[[.,.],.]],[[.,.],[.,.]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]=>[[[[.,.],[.,.]],[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[.,[[[[.,.],[.,.]],[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0]=>[[[[[.,.],.],[.,.]],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[.,[[[[[.,.],.],[.,.]],[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[.,[[[[[.,.],[.,.]],.],[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[[[[[[.,.],.],.],.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[.,[[[[[[.,.],.],.],.],[.,.]],[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[.,[[[[.,.],.],[.,.]],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[.,[.,[[[[.,.],.],[.,.]],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[[[[.,.],[.,.]],[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],[[.,.],[.,.]]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[[[.,.],.],.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.],.]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[.,.],[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[.,.],[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[[[[[[.,.],[[[[.,.],.],.],.]],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[[[[[[.,[.,.]],[[[.,.],.],.]],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,.],[.,[[[.,.],[.,.]],[.,.]]]],[[.,.],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],[[.,.],.]],[[.,.],[.,.]]],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[.,.],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[[.,.],[[[[[[.,.],.],.],.],.],.]],.],.],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],[.,.]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],[[.,.],.]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0,0]=>[[[[.,.],[.,.]],[[.,.],.]],[[[.,.],.],[.,.]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]],.]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[[[[[[.,[.,.]],.],.],.],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[[[[[.,[.,[.,.]]],.],.],[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]],.]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]],.]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[[[[[.,.],.],.],[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],.],.]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[[[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],.]]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,.],[[[.,.],.],.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[.,[.,[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0]=>[[[[[.,.],.],[.,.]],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,.]],[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[.,[[[[[.,.],.],.],[.,.]],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[.,[[[[.,[.,.]],.],[.,.]],[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],.]]]]
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[.,.],.],[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,.],[.,[[.,.],[.,[[.,.],[.,.]]]]]]],.]
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[.,[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[.,[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[.,[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[[[[.,.],[[[[[.,.],.],.],.],.]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[.,[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[.,[.,[.,[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[.,.],[.,[[[[.,.],.],[.,.]],[[.,.],[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[.,[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[.,[[[.,.],[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[[[[.,.],.],[.,.]],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[.,[[[.,[.,.]],.],[[.,.],[.,[[.,[.,.]],.]]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[.,[.,.]],.],[[.,.],[.,[[.,[.,[.,.]]],.]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[.,.],[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]],.]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[.,[[.,[[[.,[[[[.,.],.],[.,.]],.]],.],.]],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[[.,.],.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[.,[.,[[[.,[.,.]],[.,.]],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0,0]=>[[[[.,.],[.,.]],[[.,.],.]],[[.,[.,.]],[.,.]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]=>[[[[.,.],[.,.]],[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],.],[[.,.],.]],[[[.,[.,.]],.],.]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[[[.,[[[.,.],[.,.]],.]],[[[.,[.,.]],.],.]],.]
[1,0,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[.,[.,[[[[[.,.],.],.],[.,.]],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[[[[[.,.],.],.],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[.,[[[[.,.],.],[.,.]],[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[[[[[.,.],.],.],[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[.,.],[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],[[.,.],.]]],[[.,.],[.,.]]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0,0]=>[[[[[.,.],.],[.,.]],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0]=>[[[[.,.],[.,.]],[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[[[[[[.,.],.],[.,.]],[.,.]],[[.,.],[.,.]]],.]
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],[.,[.,.]]],[[.,.],[.,.]]],.]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[[[[[.,.],[.,.]],.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]],.]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0]=>[.,[[[.,[.,.]],[.,.]],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[[[[[[.,.],.],[.,.]],[[.,.],[[.,.],.]]],.],.]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[[[[[.,.],.],[.,.]],[[.,.],[[[.,.],.],.]]],.]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[[.,[[[.,.],[.,.]],.]],[.,[[[.,.],.],.]]],.]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[[[.,[[[.,.],[.,.]],[.,[.,.]]]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0]=>[[[.,[[[.,.],.],[.,.]]],[.,[[[.,.],.],.]]],.]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[[[.,[[[.,.],.],[.,.]]],[[[.,[.,.]],.],.]],.]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[[[.,[[[.,.],[.,.]],.]],.],.],[.,[.,.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[[[.,[[[.,.],.],[.,.]]],.],.],[.,[.,.]]],.]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[[[[[.,[[[.,.],.],.]],[.,.]],.],[.,[.,.]]],.]
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>[[[[[.,[.,.]],[.,.]],.],[.,[[[.,.],.],.]]],.]
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[[[[[.,[.,.]],[.,.]],.],[[[.,[.,.]],.],.]],.]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[[[.,[[[.,.],.],.]],.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[[[[[.,[.,.]],[.,.]],[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0]=>[[[[[.,[.,.]],.],[.,.]],[.,[[[.,.],.],.]]],.]
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[[[[[.,[.,.]],.],[.,.]],[[[.,[.,.]],.],.]],.]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,[.,.]],[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[[.,[.,.]],[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[[[[.,[[[.,.],.],.]],.],.],[.,.]]]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[[.,[.,.]],[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[[.,[.,.]],[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[[[.,.],.],.]],[[.,[[[.,.],.],.]],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[.,[[[.,.],.],.]],[[[[.,[.,.]],.],.],[.,.]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]=>[[.,[[[.,.],[[.,[.,.]],[.,.]]],.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[[.,[[[.,.],[[.,.],.]],.]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>[[.,[[[.,.],[[.,.],.]],.]],[[[.,[.,.]],.],.]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[[.,[[[.,.],.],[[.,[.,.]],[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[[.,[[[.,.],[[.,.],.]],[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[[.,[[[.,.],.],[[.,.],.]]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[[.,[[[.,.],.],[[.,.],.]]],[[[.,[.,.]],.],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[[.,[.,.]],.],.],[[.,[[[.,.],.],.]],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[[.,[.,.]],.],.],[[[[.,[.,.]],.],.],[.,.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[[[.,[[[.,.],.],.]],.],.],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[[.,[[[.,.],[[.,.],.]],.]],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[[.,[[[.,.],.],[[.,.],.]]],.],.],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[[[[.,[.,.]],[[.,[.,.]],[.,.]]],.],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[[.,[[[.,.],.],.]],[[.,.],.]],.],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[[.,.],.]],.],[.,[[[.,.],.],.]]]
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[[.,.],.]],.],[[[.,[.,.]],.],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[[[.,[.,.]],.],[[.,[.,.]],[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[[.,[[[.,.],.],.]],.],[[.,.],.]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[[.,.],.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],.],[[.,.],.]],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[[[[[.,[.,.]],[.,.]],[[.,.],[[.,.],.]]],.],.]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,0]=>[[[[.,[.,.]],[.,.]],[[.,.],[[[.,.],.],.]]],.]
[1,1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[[.,.],[[[[[.,.],.],.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[.,[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]]
[1,1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[[.,[[[[.,.],[.,.]],.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[[.,[[[[.,.],.],[.,.]],[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[[[[[.,.],[.,.]],.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]=>[[[[.,.],[.,.]],[[.,.],[.,[.,.]]]],[[.,.],[.,.]]]
[1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[[[[.,.],[.,.]],[[[.,.],.],.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[.,[[[[.,.],[.,.]],[[[.,.],.],.]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0]=>[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[[.,.],[.,.]],[[[[[[[.,.],[.,.]],.],.],.],.],.]]
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[[.,[.,[.,[.,[.,.]]]]],[.,.]],[[.,.],[.,.]]],.]
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[[[[[[.,.],[.,.]],.],.],.],.]]]
[1,1,0,1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[[.,[.,[.,[.,.]]]],[.,.]],[[[.,.],[.,.]],.]],.]
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[[[[[.,.],[.,.]],.],.],.]]]]
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],.],[[[[[[.,.],[.,.]],.],.],.],.]]
[1,1,0,1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[[.,[.,[.,.]]],[.,.]],[[[[.,.],[.,.]],.],.]],.]
[1,1,0,1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[[.,[.,[.,[.,.]]]],[.,.]],[.,[[.,.],[.,.]]]],.]
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]]
[1,1,1,1,0,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],.],[.,[[[[[.,.],[.,.]],.],.],.]]]
[1,1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[.,[[.,.],[.,.]]],[[[[[[.,.],[.,.]],.],.],.],.]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[[[.,[.,.]],[.,.]],[[[[[.,.],[.,.]],.],.],.]],.]
[1,1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[[.,[.,[.,.]]],[.,.]],[.,[[[.,.],[.,.]],.]]],.]
[1,1,1,0,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]],[[.,.],[.,.]]]
[1,1,0,1,1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[[[.,[.,[.,[.,.]]]],[.,.]],.],[[.,.],[.,.]]],.]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]
[1,1,1,1,0,1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],.],[.,[.,[[[[.,.],[.,.]],.],.]]]]
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],.],.],[[[[[.,.],[.,.]],.],.],.]]
[1,1,1,0,1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[.,[[.,.],[.,.]]],[.,[[[[[.,.],[.,.]],.],.],.]]]
[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[[[[[[.,.],[.,.]],.],.],.],.]],.]
[1,1,1,1,0,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[[[[.,[.,.]],[.,.]],.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[[[.,[.,.]],[.,.]],[.,[[[[.,.],[.,.]],.],.]]],.]
[1,1,1,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],[[.,.],[.,.]]]
[1,1,0,1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[[.,[.,[.,.]]],[.,.]],[.,[.,[[.,.],[.,.]]]]],.]
[1,1,1,0,1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[.,[.,[[.,[.,[.,.]]],[.,.]]]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[[[.,[.,[.,.]]],[.,.]],.],[[[.,.],[.,.]],.]],.]
[1,1,0,1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[.,[[.,[.,[.,[.,.]]]],[.,.]]],[[.,.],[.,.]]],.]
[1,1,1,1,0,1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],.],[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,1,1,1,0,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],.],.],[.,[[[[.,.],[.,.]],.],.]]]
[1,1,1,0,1,1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[.,[[.,.],[.,.]]],[.,[.,[[[[.,.],[.,.]],.],.]]]]
[1,1,1,0,1,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],.]],[[[[[.,.],[.,.]],.],.],.]]
[1,1,0,1,1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,[[[[[.,.],[.,.]],.],.],.]]],.]
[1,1,1,1,0,1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[[[[[.,[.,.]],[.,.]],.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[[[[[.,[.,.]],[.,.]],.],.],.],[[[.,.],[.,.]],.]]
[1,1,0,1,1,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[[[.,[.,.]],[.,.]],[.,[.,[[[.,.],[.,.]],.]]]],.]
[1,1,1,0,1,0,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[.,[.,[[.,[.,.]],[.,.]]]],[[[[.,.],[.,.]],.],.]]
[1,1,0,1,1,1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[[[[.,[.,.]],[.,.]],.],[[[[.,.],[.,.]],.],.]],.]
[1,1,1,0,1,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[.,[[[[.,[.,[.,.]]],[.,.]],.],.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[.,[.,[[.,[.,[.,.]]],[.,.]]]],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[[[.,[.,[.,.]]],[.,.]],.],[.,[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[.,[[.,[.,[.,.]]],[.,.]]],[[[.,.],[.,.]],.]],.]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[[.,.],.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[[[.,[[[.,.],[.,[.,.]]],.]],[.,[[[.,.],.],.]]],.]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[.,[[[.,[[[.,.],[.,.]],.]],[.,[.,.]]],.]],.],.]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>[[[.,[[[.,.],[.,[.,.]]],.]],[[[.,[.,.]],.],.]],.]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[.,[[[.,[[[.,.],.],[.,.]]],[.,[.,.]]],.]],.],.]
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>[[[.,[[[.,.],.],[.,[.,.]]]],[.,[[[.,.],.],.]]],.]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>[[[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]],[.,[.,.]]],.]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[[[.,[[[[[.,[.,.]],[.,.]],.],[.,[.,.]]],.]],.],.]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[.,[[[[[.,[[[.,.],.],.]],.],.],[.,.]],.]],.],.]
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0]=>[[[[[.,[.,.]],[.,[.,.]]],.],[.,[[[.,.],.],.]]],.]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0]=>[[[.,[[[.,.],.],[.,[.,.]]]],[[[.,[.,.]],.],.]],.]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[[[[[.,[[[.,.],[.,[.,.]]],.]],.],.],[.,[.,.]]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[[[.,[[[.,.],[.,[[[.,.],.],.]]],.]],[.,[.,.]]],.]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[.,[[.,[[[.,.],[[.,.],.]],.]],[.,[.,.]]]],.],.]
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[[[.,[[[[[.,[.,.]],.],[.,.]],[.,[.,.]]],.]],.],.]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,[.,.]],[.,[[[.,[[[.,.],.],.]],[.,.]],.]]],.]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,[[.,[.,.]],[[.,[[[.,.],.],.]],[.,.]]]],.],.]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],[.,[[[.,.],.],.]]]
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0]=>[[[[[.,[.,.]],[.,[.,.]]],.],[[[.,[.,.]],.],.]],.]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0]=>[[[[[.,[[[.,.],.],.]],[.,[.,.]]],.],[.,[.,.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[[[[[.,[[[.,.],.],[.,[.,.]]]],.],.],[.,[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[[.,[.,.]],[[.,[[[.,.],[.,[.,.]]],.]],[.,[.,.]]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[.,[[[.,.],.],[.,[[[.,.],.],.]]]],[.,[.,.]]],.]
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[.,[[.,[[[.,.],.],[[.,.],.]]],[.,[.,.]]]],.],.]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,[[[.,.],.],.]],[.,[[[.,[.,.]],[.,.]],.]]],.]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[[.,[[.,[[[.,.],.],.]],[[.,[.,.]],[.,.]]]],.],.]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[.,[.,.]],[.,[[[[[.,[.,.]],.],.],[.,.]],.]]],.]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[.,[[.,[.,.]],[[[[.,[.,.]],.],.],[.,.]]]],.],.]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[[.,[[[.,[[[.,.],.],.]],[.,.]],.]],.]]
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],[[[.,[.,.]],.],.]]
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0]=>[[[[[.,[.,.]],.],[.,[.,.]]],[.,[[[.,.],.],.]]],.]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[[[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[[[[[.,[[[.,.],.],.]],.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[[.,[.,.]],[[.,[[[.,.],.],[.,[.,.]]]],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[[[[[.,[.,.]],[.,[[[.,.],.],.]]],.],[.,[.,.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[[[.,[[[.,.],.],.]],.],.],[.,[[[.,.],.],.]]],.]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,[[[.,.],.],.]],[.,[[.,[.,.]],[[.,.],.]]]],.]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[[.,[[[[.,[.,.]],[[.,.],.]],.],[.,[.,.]]]],.],.]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,[.,.]],[.,[[.,[[[.,.],.],.]],[[.,.],.]]]],.]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,[[[[.,[[[.,.],.],.]],.],.],[[.,.],.]]],.],.]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[[[.,[.,.]],.],.],[.,[[[.,[.,.]],[.,.]],.]]],.]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[[.,[.,.]],[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]],.]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[[.,[[[[.,[.,.]],.],.],[[.,[.,.]],[.,.]]]],.],.]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[.,[.,.]],[[.,[[[[[.,[.,.]],.],.],[.,.]],.]],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[[.,[.,.]],.],[[.,[[[.,.],.],.]],.]],[.,[.,.]]]
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],.],[[.,.],.]],[[[.,[.,.]],.],.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[[.,[.,.]],[[.,[[[.,.],.],.]],.]],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],.],[[.,.],.]],[.,[[[.,.],.],.]]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[[[.,[[[.,.],.],.]],.],.],[[.,[[[.,.],.],.]],.]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[[.,.],.],[[.,[[[.,.],.],.]],.]]],[.,[.,.]]]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[[.,.],.]],[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[[.,.],.]],.],[[[.,[.,.]],.],.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[[.,[.,.]],.],.],[[.,[.,.]],[.,[[[.,.],.],.]]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[[.,.],[[.,[[[.,.],.],.]],.]],.]],[.,[.,.]]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[[[[.,[.,.]],.],[.,[[[.,.],.],.]]],[.,[.,.]]],.]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[[.,[.,.]],.],.],[[.,[[.,[.,.]],[[.,.],.]]],.]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[[[.,[[[.,.],.],.]],.],[[.,.],.]],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[[.,.],.]],.],[.,[[[.,.],.],.]]]]
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,[[[[.,[.,.]],.],[[.,.],.]],[.,[.,.]]]],.],.]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[[[.,.],.],[[.,.],.]]],[[[.,[.,.]],.],.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[[.,[.,.]],.],.],[[.,[[[.,[.,.]],[.,.]],.]],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[[.,.],.],.]],[[.,[.,.]],[.,[[[.,.],.],.]]]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[[[.,[.,.]],.],.],[.,[[[.,.],.],.]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[[[.,[.,.]],.],[[.,[.,.]],[.,.]]],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[[.,.],.],.]],[[.,[[.,[.,.]],[[.,.],.]]],.]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[[[.,[[[.,.],.],.]],[[.,.],.]],.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[[[.,[.,.]],.],.],[[.,.],.]]],.]]
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[[[.,[[[.,.],.],[[.,.],.]]],.],.],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[.,[[.,[[[.,.],.],[[.,.],.]]],[.,[[[.,.],.],.]]]]
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[.,[[[[[.,[.,.]],.],[.,.]],[[[.,[.,.]],.],.]],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[[.,.],.],.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[.,[[[.,.],.],.]],[.,[[[.,.],.],.]]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[[[.,[.,.]],[[.,[.,.]],[.,.]]],.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,.]],[.,[[.,[.,.]],[[.,.],.]]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[[[.,[.,.]],.],.],[.,[[.,[.,.]],[[.,.],.]]]],.]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,[[[.,.],.],.]],[[.,.],.]]],.]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[[[.,[[[.,.],[[.,.],.]],.]],.],.],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[[[.,.],[[.,.],.]],[.,[.,.]]]],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],[.,[[[[.,[.,.]],.],.],[[.,.],.]]]],.]
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>[.,[[.,[[[.,.],[[.,.],.]],.]],[[[.,[.,.]],.],.]]]
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0]=>[.,[[[[[.,[.,.]],.],[.,.]],[.,[[[.,.],.],.]]],.]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[[[.,[[[.,.],.],.]],.],.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[[.,.],.],[[.,[.,.]],[.,.]]]],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[[[.,[.,.]],.],.],[[.,[[[.,.],.],.]],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[[[.,[.,.]],.],.],[[[[.,[.,.]],.],.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[[.,.],[[.,[.,.]],[.,.]]],.]],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[[[.,.],.],.]],[[.,[[[.,.],.],.]],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[[[.,[.,.]],.],.],[[.,[[[.,.],.],.]],[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[.,[[[.,.],.],.]],[[[[.,[.,.]],.],.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[.,[[.,[.,.]],[[[[.,[[[.,.],.],.]],.],.],[.,.]]]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[.,[[[[[.,[[[.,.],.],.]],.],[.,.]],[.,[.,.]]],.]]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[[.,[.,.]],[[[[.,[.,.]],[.,[.,.]]],.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[[[[.,[[[.,.],[[.,[.,.]],.]],.]],.],.],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[.,[[[.,.],.],.]],[[.,[[[.,.],.],.]],[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[.,[[.,[.,.]],[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[.,[[[[[.,[[[.,.],.],.]],[.,.]],.],[.,[.,.]]],.]]
[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[.,[[[[.,.],[.,.]],[[.,.],.]],[[.,.],[.,.]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[[.,.],.],[.,.]],[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[.,.],.],[.,[[[[.,.],.],[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],.],[.,.]],[[.,.],[.,[[.,[[.,.],.]],.]]]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[[.,[[[[.,.],.],[.,.]],[[.,.],[.,[[.,.],.]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[.,.],[.,[[[.,.],[.,.]],[[.,.],.]]]],[[.,.],.]]
[1,1,0,0,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[.,[[.,[[[[.,.],.],[.,.]],[[.,.],[.,.]]]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[.,[[[.,[[[.,.],[.,.]],.]],[.,[[[.,.],.],.]]],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[.,[[[.,[[[.,.],[.,.]],.]],[[[.,[.,.]],.],.]],.]]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[.,[[[.,[[[.,.],[.,.]],[.,[.,.]]]],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0]=>[.,[[[.,[[[.,.],.],[.,.]]],[.,[[[.,.],.],.]]],.]]
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[.,[[[.,[[[.,.],.],[.,.]]],[[[.,[.,.]],.],.]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[[[[.,[[[.,.],[.,.]],.]],.],.],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[.,[[[[[.,[[[.,.],.],[.,.]]],.],.],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>[.,[[[[[.,[.,.]],[.,.]],.],[.,[[[.,.],.],.]]],.]]
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[.,[[[[[.,[.,.]],[.,.]],.],[[[.,[.,.]],.],.]],.]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[.,[[[[[.,[.,.]],[.,.]],[.,[.,.]]],[.,[.,.]]],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[.,[.,.]],[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[.,[[.,[.,.]],[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[.,[[.,[.,.]],[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[.,[[.,[[[.,.],[[.,.],.]],.]],[.,[[[.,.],.],.]]]]
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[[[[[.,[.,.]],.],[.,[.,.]]],[[[.,[.,.]],.],.]],.]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]],.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[.,[.,.]],[.,[[[.,[.,.]],[.,.]],.]]]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[.,.]],[[[[.,[[[.,.],.],.]],.],.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[[.,[.,.]],[[[[.,[.,.]],.],[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[[[.,[.,.]],.],.],[[[[.,[.,.]],.],.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[[[[.,[[[.,.],.],.]],.],.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[[[[.,[[[.,.],.],[[.,[.,.]],.]]],.],.],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[[.,[.,.]],.],[[.,[.,.]],[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[[.,[[[.,.],.],.]],.],[[.,[.,.]],.]],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[[.,[.,.]],.]],[[[.,[.,.]],.],.]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[[.,[.,.]],.]],[.,[[[.,.],.],.]]]
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],.],[.,[[[.,.],.],.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[[.,[[[.,.],.],.]],[[.,[.,.]],.]],.],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[[[.,.],.],.]],[[[[.,[.,.]],.],.],[.,[.,.]]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],.],[[.,[.,.]],.]]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],.],[[.,[.,.]],.]]],[[[.,[.,.]],.],.]]
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],.],[[[.,[.,.]],.],.]]
[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],[[[.,.],.],[.,.]]]
[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[[[.,[[[.,.],[.,.]],.]],[.,[[[.,.],[.,.]],.]]],.]
[1,1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[[.,[.,[[[.,.],[.,.]],.]]],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,1,1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[[[[[[.,.],[.,.]],.],.],[.,[[[.,.],[.,.]],.]]],.]
[1,1,1,0,1,1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[[.,[[[[.,.],[.,.]],.],.]],[.,[[[.,.],[.,.]],.]]]
[1,1,1,1,0,1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[[[[[[.,.],[.,.]],.],.],.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,1,0,1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[[[.,[[.,.],[.,.]]],[.,[.,[[[.,.],[.,.]],.]]]],.]
[1,1,1,0,1,0,1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,0,1,1,1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],.],[.,[.,[[[.,.],[.,.]],.]]]],.]
[1,1,1,0,1,1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],.]],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,1,0,1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],.],.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,0,1,1,1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,[.,[.,[[[.,.],[.,.]],.]]]]],.]
[1,1,1,0,1,1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[[.,[[.,.],[.,.]]],[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[[.,[[[.,.],[.,.]],.]],[[[[.,.],[.,.]],.],.]],.]
[1,1,1,0,1,0,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[.,[.,[[[.,.],[.,.]],.]]],[[[[.,.],[.,.]],.],.]]
[1,1,0,1,1,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[[[[[.,.],[.,.]],.],.],[[[[.,.],[.,.]],.],.]],.]
[1,1,1,0,1,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[.,[[[[.,.],[.,.]],.],.]],[[[[.,.],[.,.]],.],.]]
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[[[[[.,.],[.,.]],.],.],.],[[[[.,.],[.,.]],.],.]]
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[[.,[[.,.],[.,.]]],[.,[[[[.,.],[.,.]],.],.]]],.]
[1,1,1,0,1,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[.,[.,[[.,.],[.,.]]]],[.,[[[[.,.],[.,.]],.],.]]]
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],.],[.,[[[[.,.],[.,.]],.],.]]],.]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],.]],[.,[[[[.,.],[.,.]],.],.]]]
[1,1,0,1,1,1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,[.,[[[[.,.],[.,.]],.],.]]]],.]
[1,1,0,1,1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[[.,[[.,.],[.,.]]],[[[[[.,.],[.,.]],.],.],.]],.]
[1,1,1,0,1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[.,[.,[[.,.],[.,.]]]],[[[[[.,.],[.,.]],.],.],.]]
[1,1,0,1,1,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],.],[[[[[.,.],[.,.]],.],.],.]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],[.,[[.,.],[.,.]]]],.]
[1,1,1,0,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[[.,[.,[[[.,[.,.]],[.,.]],.]]],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[[[[[[.,[.,.]],[.,.]],.],.],[.,[[.,.],[.,.]]]],.]
[1,1,1,0,1,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[[.,[[[[.,[.,.]],[.,.]],.],.]],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[[[[[[.,[.,.]],[.,.]],.],.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[[[.,[[.,[.,.]],[.,.]]],[.,[.,[[.,.],[.,.]]]]],.]
[1,1,1,0,1,0,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[[[[[.,[.,.]],[.,.]],.],[.,[.,[[.,.],[.,.]]]]],.]
[1,1,1,0,1,1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[[[[.,[.,.]],[.,.]],[.,[.,[.,[[.,.],[.,.]]]]]],.]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],[[[.,.],[.,.]],.]],.]
[1,1,1,0,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[.,[.,[[[.,[.,.]],[.,.]],.]]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[[[[[.,[.,.]],[.,.]],.],.],[[[.,.],[.,.]],.]],.]
[1,1,1,0,1,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[.,[[[[.,[.,.]],[.,.]],.],.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[[.,[[.,[.,.]],[.,.]]],[.,[[[.,.],[.,.]],.]]],.]
[1,1,1,0,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[[[[.,[.,.]],[.,.]],.],[.,[[[.,.],[.,.]],.]]],.]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,[[[.,.],[.,.]],.]]]
[1,1,1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[[[[.,[.,.]],[.,.]],.],.],[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,1,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,1,0,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[[[.,[.,.]],[.,.]],.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,1,0,1,1,0,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[[.,[[.,[.,.]],[.,.]]],[[[[.,.],[.,.]],.],.]],.]
[1,1,1,0,1,1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[[[[.,.],[.,.]],.],.]]
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[[[[.,[.,.]],[.,.]],.],.],[[[[.,.],[.,.]],.],.]]
[1,1,1,0,1,1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[.,[[.,[.,.]],[.,.]]],[.,[[[[.,.],[.,.]],.],.]]]
[1,1,1,1,0,1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[[[.,[.,.]],[.,.]],.],[.,[[[[.,.],[.,.]],.],.]]]
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[.,[[[[.,.],[.,.]],.],.]]]]
[1,1,1,0,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[.,[[.,[.,.]],[.,.]]],[[[[[.,.],[.,.]],.],.],.]]
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[[[.,[.,.]],[.,.]],.],[[[[[.,.],[.,.]],.],.],.]]
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[[[[[.,.],[.,.]],.],.],.]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[[.,[.,.]],[.,.]],[[[[[[.,.],[.,.]],.],.],.],.]]
[1,1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[.,[[[.,[.,[.,.]]],[.,.]],.]],[[.,.],[.,.]]],.]
[1,1,1,0,1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]],[[.,.],[.,.]]]
[1,1,0,1,1,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[[[[.,[.,[.,.]]],[.,.]],.],.],[[.,.],[.,.]]],.]
[1,1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[.,[[.,[.,[.,.]]],[.,.]]],[.,[[.,.],[.,.]]]],.]
[1,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[.,[[[.,[.,[.,.]]],[.,.]],.]],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[.,[[[.,[.,[.,.]]],[.,.]],.]],[[[.,.],[.,.]],.]]
[1,1,1,1,0,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],[[[.,.],[.,.]],.]]
[1,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,[[[.,.],[.,.]],.]]]
[1,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,[[[.,.],[.,.]],.]]]
[1,1,1,1,1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,0,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[.,[[.,[.,[.,.]]],[.,.]]],[[[[.,.],[.,.]],.],.]]
[1,1,1,1,0,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[[.,[.,[.,.]]],[.,.]],.],[[[[.,.],[.,.]],.],.]]
[1,1,1,1,1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[.,[.,[.,.]]],[.,.]],[.,[[[[.,.],[.,.]],.],.]]]
[1,1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[.,[.,[.,.]]],[.,.]],[[[[[.,.],[.,.]],.],.],.]]
[1,1,1,0,1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[[[.,[.,[.,[.,.]]]],[.,.]],.],.],[[.,.],[.,.]]]
[1,1,1,0,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],[[[.,.],[.,.]],.]]
[1,1,1,1,0,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],[[[.,.],[.,.]],.]]
[1,1,1,1,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[.,[.,[.,[.,.]]]],[.,.]],[[[[.,.],[.,.]],.],.]]
[1,1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],[[.,.],[.,.]]]
[1,1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],[[[.,.],[.,.]],.]]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]],.]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],.],[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[[[.,.],.],[.,[[.,[[.,[[.,.],.]],.]],.]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],[.,[[.,[[.,[[.,.],.]],.]],.]]],[[.,.],.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[[.,[[.,[[[.,.],.],[.,[[.,[[.,.],.]],.]]]],.]],.]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],.],[.,[[[.,.],.],[.,[[.,[[.,.],.]],.]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0]=>[[.,[[[.,.],[.,[[.,[[.,.],.]],.]]],[[.,.],.]]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[[.,[[.,[[[.,.],.],[.,[[.,.],.]]]],.]],.]],.]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],.],[.,[[.,[[[.,.],.],[.,[[.,.],.]]]],.]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[[[.,.],.],[.,[[[.,.],.],[.,[[.,.],.]]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[[[.,.],.],[.,[[.,.],.]]]]],[[.,.],.]]
[1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[.,[[.,[[[.,.],[.,[[.,.],.]]],[[.,.],.]]],.]],.]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[[.,.],.],[.,[[[.,.],[.,[[.,.],.]]],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[[.,[[.,[[.,[[[.,.],.],[.,.]]],.]],.]],.]],.]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],.],[.,[[.,[[.,[[[.,.],.],[.,.]]],.]],.]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[[[.,.],.],[.,[[.,[[[.,.],.],[.,.]]],.]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,[[.,[[[.,.],.],[.,.]]],.]]],[[.,.],.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[[.,[[[.,.],.],[.,[[[.,.],.],[.,.]]]]],.]],.]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],.],[.,[[[.,.],.],[.,[[[.,.],.],[.,.]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[[[.,.],[.,[[[.,.],.],[.,.]]]],[[.,.],.]]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[[.,[[.,[[[.,.],[.,.]],[[.,.],.]]],.]],.]],.]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[.,.],.],[.,[[.,[[[.,.],[.,.]],[[.,.],.]]],.]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[[[.,.],.],[.,[[[.,.],[.,.]],[[.,.],.]]]]],.]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,.],[[.,[.,.]],.]],[[[.,[.,.]],.],[[.,.],.]]]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[.,[[.,[[.,[[.,[[.,[[[.,.],.],.]],.]],.]],.]],.]]
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]],.]
[1,1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[.,[[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]],.]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0]=>[[[[.,.],[.,.]],[[.,[.,.]],[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0,0]=>[[[[.,.],[.,.]],[[.,.],.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],[[.,.],.]]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[.,[[[[.,[.,.]],.],[[.,[.,.]],.]],[[.,[.,.]],.]]]
[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[.,[[.,.],[.,[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]]]]
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[[.,[[[.,.],[.,.]],.]],[.,[[[.,.],.],.]]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[[[[.,[.,.]],.],[[[.,.],.],.]],[[[.,[.,.]],.],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[.,[[[.,[[[.,.],.],.]],[.,[[.,[.,.]],[.,.]]]],.]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0]=>[[[.,[[[.,.],[[.,[.,.]],[.,.]]],.]],[[.,.],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[.,[[[.,[[[.,.],[.,[.,.]]],.]],[.,[[.,.],.]]],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[.,[[[.,[[[.,.],[.,[.,.]]],.]],[[[.,.],.],.]],.]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[.,[[.,[[[.,.],[.,[.,.]]],.]],[.,[[[.,.],.],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[.,[.,[[[.,[.,[[[.,[.,.]],.],.]]],.],.]]],.],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[.,[[[.,[[[.,.],[.,.]],.]],[.,[[.,.],.]]],.]],.]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[.,.]],[.,[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,.]],[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[[.,[.,.]],[[.,[.,.]],[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[[[.,.],[.,.]],.]],[[.,.],[.,.]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,.]],[[.,.],.]],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]]
[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,.],[[[[.,[.,.]],.],[[.,.],.]],[.,.]]]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[[.,[.,.]],.],[[.,.],[[.,.],.]]],[.,.]]]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[[.,[.,.]],.],[[.,.],.]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[.,[[[.,[.,.]],.],[[.,.],.]]],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[[.,[.,.]],.],[[.,.],[[.,.],[[.,.],.]]]],[.,.]]
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[.,[.,.]],.],[[.,.],.]],[[.,[.,.]],.]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[[.,[.,.]],.],[[.,.],[[.,.],.]]],[.,.]],[.,.]]
[1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[[[.,[.,.]],.],[[.,.],.]],[.,.]],[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[.,[.,.]],.],[[.,.],.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[.,[[[.,[.,.]],.],[[.,.],[[.,.],.]]]],.],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[[[[[.,[.,.]],.],[[.,.],.]],[.,.]],[.,.]]],.]
[1,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[.,[[[.,[.,.]],.],[[.,.],.]]],.],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[[[.,[[[.,[.,.]],.],[[.,.],.]]],.],[.,.]]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[[[.,[.,.]],.],[[.,.],.]],[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[.,[.,.]],.],[[.,.],[[.,.],.]]],[[.,[.,.]],.]]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],.],[[.,.],.]],[[.,[[.,[.,.]],.]],.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,[.,.]],.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[[.,[.,.]],.],[[.,.],.]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[.,.],[[[.,[.,.]],.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,.],[[.,.],[[[.,[.,.]],.],[[.,.],.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],.],[[[.,[.,.]],.],[[.,.],.]]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[[.,[.,.]],.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[.,.],[[[.,[.,.]],.],[[.,.],.]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[.,[.,.]],.],[[[.,[.,.]],.],[[.,.],.]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],.],[[[.,[.,.]],.],[[.,.],.]]]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],.],[[.,.],[[.,.],[[.,.],.]]]]],.]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[[[[.,[.,.]],.],[[.,.],.]],[[.,[.,.]],.]]],.]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,.],[[[.,[.,.]],.],[[.,.],[[.,.],.]]]]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[[.,.],[[.,.],[[[.,[.,.]],.],[[.,.],.]]]]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],.],[[[.,[.,.]],.],[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[.,[[[.,[.,.]],.],[[.,.],[[.,.],.]]]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[[.,[.,.]],.],[[.,.],.]]]],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,.],[[.,[[[.,[.,.]],.],[[.,.],.]]],.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[.,[[[.,[.,.]],.],[[.,.],.]]],.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[[[.,[.,.]],.],[[.,.],[[.,.],.]]]],.]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[[.,.],[[[.,[.,.]],.],[[.,.],.]]]],.]],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[[.,.],[[.,[[[.,[.,.]],.],[[.,.],.]]],.]]],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[[.,[.,.]],.],[[.,.],.]]],.]],.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[[.,[[[.,[.,.]],.],[[.,.],.]]],.]],.]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]],.]
[1,1,0,0,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[[.,.],[[[[.,[.,.]],.],[[.,.],.]],[.,.]]]],.]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[[[[.,[.,.]],.],[[.,.],[[.,.],.]]],[.,.]]],.]
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,[[[[.,[.,.]],.],[[.,.],.]],[.,.]]],.],[.,.]]
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,[[.,[[[.,[.,.]],.],[[.,.],.]]],.]],.],[.,.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,[[[.,[.,.]],.],[[.,.],.]]],.],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[.,[[.,[.,.]],.]],.],[[.,.],[[.,.],.]]],[.,.]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[[.,[[.,[.,.]],.]],.],[[.,.],.]],[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[.,[[.,[.,.]],.]],.],[[.,.],.]],[[.,[.,.]],.]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,[[[[.,[[.,[.,.]],.]],.],[[.,.],.]],[.,.]]],.]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[.,[[.,[[.,[.,.]],.]],.]],.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,[[[.,[[.,[[.,[.,.]],.]],.]],.],[[.,.],.]]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[[[.,[.,.]],.],[[.,.],.]],[.,.]]],.]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,[[.,[.,.]],.]],.],[[.,.],[[.,.],.]]]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[[.,[[.,[.,.]],.]],.],[[.,.],.]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[.,[[.,[[.,[.,.]],.]],.]],.],[[.,.],.]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,.],[[[.,[[.,[.,.]],.]],.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,.],[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[[[.,[.,.]],.],[[.,[[.,.],.]],.]],[.,.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[[.,[.,.]],.],[[.,[[.,.],[[.,.],.]]],.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[[.,[.,.]],.],[[.,.],[[.,[[.,.],.]],.]]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[[.,[.,.]],.],[[.,[[.,.],.]],.]],[.,.]],[.,.]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,[[[.,[.,.]],.],[[.,[[.,.],.]],.]]],.],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[[.,[[.,[.,.]],.]],.],[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[.,[.,.]],.],[[.,[[.,.],.]],.]],[[.,[.,.]],.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,.],[[[.,[.,.]],.],[[.,[[.,.],[[.,.],.]]],.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[[.,[.,.]],.],[[.,.],[[.,[[.,.],.]],.]]]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[[[.,[.,.]],.],[[.,[[.,.],.]],.]]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],.],[[[.,[.,.]],.],[[.,[[.,.],.]],.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],.],[[.,[[.,.],[[.,.],.]]],.]]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],.],[[.,.],[[.,[[.,.],.]],.]]]],.]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,.],[[[.,[.,.]],.],[[.,[[.,.],.]],.]]]],.]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[.,[[[.,[.,.]],.],[[.,[[.,.],.]],.]]],.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[[.,[.,.]],.],[[.,[[.,.],.]],.]]],.]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]],.]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[[[[.,[.,.]],.],[[.,.],.]],[.,.]]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[[[.,[[.,[.,.]],.]],.],[[.,.],[[.,.],.]]]],.]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[.,[[[.,[[.,[.,.]],.]],.],[[.,.],.]]],.],[.,.]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]],.]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,[[.,.],[[[.,[[.,[.,.]],.]],.],[[.,.],.]]]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]],.]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[[.,[.,.]],.],[[.,[[.,.],.]],.]],[.,.]]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],.],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],.],[[.,.],[[.,[[.,.],.]],.]]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[.,[[.,[.,.]],.]],.],[[.,[[.,.],.]],.]],[.,.]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],[[.,[[.,.],.]],.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]]
[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]=>[[.,.],[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[[.,[[.,[.,.]],.]],.],[[.,[[.,.],.]],.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,.],[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,.]],.],[[.,[[.,[[.,.],.]],.]],.]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,.]],.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[[.,[.,.]],.],[[.,[[.,[[.,.],.]],.]],.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],.],[[.,[[.,[[.,.],.]],.]],.]]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[[[.,[[.,[.,.]],.]],.],[[.,.],.]]],.]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[[.,[.,.]],.]],.],[[.,[[.,.],.]],.]]],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],.],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,.]],.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[[[[.,[[[.,.],.],.]],.],.],[[[.,[.,.]],.],[.,.]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0,0,1,0]=>[[[[.,[[[.,.],.],.]],[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[[.,.],.],.],[[[[[.,[[.,.],.]],.],.],[.,.]],.]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[.,[[[[.,[[[.,.],.],.]],.],[.,.]],[.,.]]],.],.]
[1,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[[.,[.,[[[[.,[[[.,.],.],.]],.],[.,.]],[.,.]]]],.]
[1,1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[[.,[[[.,[[[.,.],.],.]],.],.]],[[[.,.],.],[.,.]]]
[1,1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[.,[.,[[[.,.],.],[.,[.,.]]]]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[[.,[[[.,.],.],[[[[.,.],.],.],[[.,.],.]]]],[.,.]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>[[[[.,.],[[.,[[[.,.],.],.]],.]],[.,.]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0]=>[[[[.,.],[.,[.,[[[.,.],.],.]]]],[.,.]],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[[[.,.],.],[[[[[.,.],.],.],[[.,.],.]],.]],[.,.]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[[[[[.,.],[[.,[[.,.],.]],.]],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[[[[[.,.],[.,[[.,[.,.]],.]]],[.,.]],[.,[.,.]]],.]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,.],[.,[.,[[.,[.,.]],.]]]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[[[.,[.,.]],.],[[[[.,[[.,[.,.]],.]],.],.],[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[[[[[.,[[.,.],.]],[.,[.,.]]],[.,.]],.],[.,[.,.]]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[.,.],.],[[[.,[[[.,[[.,.],.]],.],.]],[.,.]],.]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0,0]=>[[[.,[[[.,[.,[[[.,.],.],.]]],[.,.]],[.,.]]],.],.]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,[[[.,[.,[[[.,.],.],.]]],[.,.]],[.,.]]]],.]
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[.,[.,[.,.]]],.],[[[[.,[[.,.],.]],.],.],[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[.,[[[.,.],.],.]],[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[[[.,.],.],[.,[[[.,.],.],.]]],[.,.]]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[.,[.,.]],[.,[.,[[[[.,.],.],[[.,.],.]],[.,.]]]]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[[.,.],[[[.,[[[.,.],.],.]],[[[.,.],.],[.,.]]],.]]
[1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[[[.,[.,.]],[[[[.,.],.],[.,[[.,.],.]]],[.,.]]],.]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]],.]
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[.,[.,.]],[.,[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[[.,[[.,[.,[[[.,.],.],.]]],.]],[[[.,.],.],[.,.]]]
[1,1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[.,[.,[[.,[.,.]],[.,[.,.]]]]],[.,.]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[[[.,[.,[.,.]]],[[[[.,.],.],.],[[.,.],.]]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[[.,.],[[.,[[[[.,.],.],[[[.,.],.],.]],[.,.]]],.]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[.,.],[.,[.,[[[[[.,.],.],[[.,.],.]],[.,.]],.]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[.,[.,.]],[[[[.,.],.],.],[[[.,.],.],.]]],[.,.]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[.,.],[[[.,[[[[.,.],.],[[.,.],.]],[.,.]]],.],.]]
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[[[.,[[[[[.,.],.],[.,[[.,.],.]]],[.,.]],.]],.],.]
[1,1,0,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[[[[.,.],.],[.,[[.,.],.]]],[.,.]],.]]],.]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[[.,.],[[[[[.,.],.],.],[[[[.,.],.],[.,.]],.]],.]]
[1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[[[.,.],[[[[[.,.],.],[.,[[.,.],.]]],[.,.]],.]],.]
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[.,.],[[[.,[[[[.,.],.],[.,[.,.]]],[.,.]]],.],.]]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[[.,.],[[.,[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]],.]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0]=>[[.,[.,[[[[.,.],.],[.,[.,[[.,.],.]]]],[.,.]]]],.]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[[[[[.,[[.,.],.]],.],.],.],[[.,[[.,.],.]],[.,.]]]
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[[[[.,[[[[.,.],.],.],[.,[.,.]]]],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[[[.,.],.],.],[[[[.,[.,.]],.],[.,.]],.]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[[[.,[[[[[.,[[.,.],.]],.],[.,.]],.],[.,.]]],.],.]
[1,1,0,0,1,0,1,1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[[.,[.,[[[[[.,[[.,.],.]],.],[.,.]],.],[.,.]]]],.]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[[.,[[[[.,[[.,.],.]],.],.],[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[[[.,[.,[[[[.,.],.],[.,[.,.]]],.]]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[[.,[[[[.,.],.],[[[.,.],.],[[.,.],.]]],.]],[.,.]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>[[[[[.,.],[[.,[[[.,.],.],.]],.]],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0]=>[[[[[.,.],[.,[.,[[[.,.],.],.]]]],.],[.,.]],[.,.]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[[[[[.,.],.],[[[[.,.],.],[[.,.],.]],.]],.],[.,.]]
[1,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[[[[[[.,.],[[.,[[.,.],.]],.]],.],[.,.]],[.,.]],.]
[1,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[[[[[[.,.],[.,[[.,[.,.]],.]]],.],[.,.]],[.,.]],.]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],[.,[.,[[.,[.,.]],.]]]],.],[.,.]],[.,.]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[[[[.,[[.,.],.]],.],.],[[.,[.,[[.,.],.]]],[.,.]]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[[[.,[[[.,.],.],[.,[.,.]]]],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[[[.,.],.],[[[[.,[.,[.,.]]],.],[.,.]],.]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[[[.,[[[[.,[[.,[.,.]],.]],[.,.]],.],[.,.]]],.],.]
[1,1,0,0,1,0,1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[[.,[.,[[[[.,[[.,[.,.]],.]],[.,.]],.],[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],[.,.]]],[.,.]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[[[[.,[[[.,[[.,.],.]],[.,[.,.]]],.]],.],.],[.,.]]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[.,[.,.]],.],[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,.]],[.,[[[.,.],.],[[.,.],.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[.,[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[.,.],.],[[[.,[.,.]],[[.,[[.,.],.]],[.,.]]],.]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,[.,.]],[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]],.]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[[.,[.,.]],[.,[[.,[.,.]],[.,[.,.]]]]],[.,.]],.]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,[[.,[.,.]],[.,[.,.]]]]]],[.,.]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[[.,[[[.,[[.,[.,.]],.]],.],[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[[[.,[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]],.],[.,.]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[.,[[.,[.,.]],.]],[[.,.],[[.,.],.]]],.],[.,.]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,[.,.]],[[[.,.],.],[[.,.],.]]]],.]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[.,.],[.,[.,[[[.,[.,.]],[[[.,.],.],[.,.]]],.]]]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[[[[.,[[.,.],.]],[[.,.],[[[.,.],.],.]]],.],[.,.]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[.,.],[[[.,[[.,[.,.]],[[[.,.],.],[.,.]]]],.],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,[[[.,[.,.]],[.,[[[.,.],.],[.,.]]]],.]],.],.]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[[[.,[.,.]],[.,[[[.,.],.],[.,.]]]],.]]],.]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[.,.],.],[[[.,.],[[[.,[[.,.],.]],[.,.]],.]],.]]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[[[.,[.,.]],[.,[[[.,.],.],[.,.]]]],.]],.]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,.],[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,.],[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]],[.,.]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[[.,[.,[[.,[.,.]],[.,[.,[[[.,.],.],[.,.]]]]]]],.]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[[[.,[.,.]],.],[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]]
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[[[[[[.,[[.,.],.]],[.,[.,.]]],.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[[[.,.],.],[[[.,[[.,[.,[[.,.],.]]],.]],[.,.]],.]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[[[.,[[[.,[.,[[.,[.,.]],.]]],[.,.]],[.,.]]],.],.]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[[.,[.,[[[.,[.,[[.,[.,.]],.]]],[.,.]],[.,.]]]],.]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[[[.,[.,[[.,.],.]]],.],[[.,[.,[[.,.],.]]],[.,.]]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[[[.,[[.,[.,.]],[.,[.,.]]]],.],.],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[.,[.,.]]],[[.,.],[.,[[[[.,.],.],[.,.]],.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,[.,[.,.]]],[.,[.,[[.,.],[[.,.],.]]]]],[.,.]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[[.,.],[[[[.,[.,[.,.]]],.],[[[.,.],.],[.,.]]],.]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[[.,[.,[.,.]]],[[.,.],[.,[[.,.],.]]]],[.,.]],.]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]],[.,.]],.]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[.,[.,[[.,.],[.,[.,.]]]]]]],[.,.]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[[[.,[.,[.,[[.,.],.]]]],.],[[.,[[.,.],.]],[.,.]]]
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[[[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.],[.,.]],[.,.]]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[.,[.,[[.,.],.]]],[[.,[.,.]],[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[.,[[[[[.,.],.],[.,.]],.],.]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[[.,[.,.]],[.,[.,[[.,.],[[[.,.],.],.]]]]],[.,.]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],.],[[[.,.],.],[[.,.],.]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[[.,.],[[.,[[[.,.],.],.]],.]]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,.],[[.,[[[.,[[[[.,.],.],[.,.]],.]],.],.]],.]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,.],[.,[.,[[[.,[[[[.,.],.],[.,.]],.]],.],.]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[[.,.],[[[[.,[.,.]],.],[[[.,.],.],[[.,.],.]]],.]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[[.,.],[[.,[[.,.],.]],.]]],[.,.]],.]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[.,[[.,.],[[.,.],[[.,[[.,[.,.]],.]],.]]]],[.,.]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[.,[[.,.],[[.,.],[.,[[.,[.,[.,.]]],.]]]]],[.,.]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[.,.],[.,[.,[[.,[.,[[[[.,.],.],[.,.]],.]]],.]]]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[[.,[[.,[.,[[.,[.,.]],.]]],.]],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,0,1,0]=>[[[.,[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]],.],[.,.]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[.,[.,[[.,[.,.]],.]]],[[.,.],[[.,.],.]]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[[[.,.],.],[[.,.],.]],.]]],.]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[.,.],[.,[.,[[[.,.],[[[[.,.],.],[.,.]],.]],.]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[.,[.,[[.,.],.]]],[[.,.],[[[[.,.],.],[.,.]],.]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[.,.],[[[.,.],[.,[[[[[.,.],.],[.,.]],.],.]]],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,[[[[.,[[[.,.],.],[.,.]]],.],.],.]]],.]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[[.,.],[[[.,[[[.,.],.],[.,.]]],.],.]]]],.]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[[.,[[.,.],.]],[[.,.],[[[[[.,.],.],[.,.]],.],.]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,.],[[[[.,.],[.,[[[[.,.],.],[.,.]],.]]],.],.]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[[[.,.],[.,[[[.,[[[.,.],.],[.,.]]],.],.]]],.],.]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[[.,.],[[.,[[[.,.],.],[.,[.,.]]]],.]]],.],.]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[.,[.,[[.,.],[[.,[[[.,.],.],[.,[.,.]]]],.]]]],.]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[[[.,.],.],[[[.,.],[[[[.,.],.],[[.,.],.]],.]],.]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[[[.,.],[[.,[[[.,.],.],[.,.]]],.]],.]],.]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,.],[[[.,.],[[.,[[.,[.,.]],.]],.]],.]],[.,.]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[[.,.],[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]],.],.]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]]],.]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[.,.],[.,[.,[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,.],[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]],[.,.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[[.,.],[.,[[[.,.],.],[.,[[.,[.,[[.,.],.]]],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,.],[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]],[.,.]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[.,[[[.,.],.],[.,[[.,[[.,.],[.,[[.,.],.]]]],.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[.,[[[.,.],.],[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[.,.],[.,[[.,.],[.,[[.,.],[.,[.,[[.,.],.]]]]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[.,[[[.,.],.],[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[.,.],[.,[[.,[.,[[[.,.],.],[.,[[.,.],.]]]]],.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[.,.],[.,[[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]],.]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[.,[[[.,.],.],[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[.,.],[.,[[.,[.,[[.,[[[.,.],.],[.,.]]],.]]],.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[[[.,.],.],[.,[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,.],.],[.,[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[.,[[.,.],[.,[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[.,[[.,.],[.,[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[[.,.],[.,[[[.,.],[.,[[.,.],[.,[.,.]]]]],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[.,[[.,[[.,.],[.,[[[.,.],.],[.,[[.,.],.]]]]]],.]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[.,[[.,[[.,.],[.,[[.,.],[.,[[.,.],[.,.]]]]]]],.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[.,.],[.,[[[.,.],.],[.,[[[.,.],.],[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[.,[[.,[[.,.],[.,[[.,[[[.,.],.],[.,.]]],.]]]],.]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[.,.],[.,[[.,[[[.,.],.],[.,[.,[[.,.],.]]]]],.]]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[.,[[.,.],[.,[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[.,[[.,[[.,[[[.,.],[.,[[.,.],.]]],[.,.]]],.]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[.,[[.,[[.,[[[.,.],.],[.,[[.,.],[.,.]]]]],.]],.]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[.,[[.,.],[.,[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]]]]
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[.,[[.,[.,[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]]],.]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[.,[[.,[.,[[[.,.],.],[.,[[[.,.],.],[.,.]]]]]],.]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[.,.],[.,[[.,.],[.,[[[.,.],[.,[.,.]]],[.,.]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[.,[[.,[[.,[[.,.],[.,[[[.,.],.],[.,.]]]]],.]],.]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[.,[[.,[.,[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]]],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[[.,[[[.,.],[.,[[.,[.,[[.,.],.]]],.]]],[.,.]]],.]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[.,[[[.,.],.],[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[.,[[[.,.],.],[.,[[.,.],[.,[.,[[.,.],.]]]]]]],.]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[[.,.],[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]]],.]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,.],[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]]],.]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[[.,.],[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]]],.]
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[.,[[.,.],[.,[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[.,[[[.,.],[.,[[.,.],[.,[.,[[.,.],.]]]]]],[.,.]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[[.,[[[.,.],[.,[[.,.],[.,[.,.]]]]],[[.,.],.]]],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[.,[[[.,.],[.,[[[.,.],.],[.,[[.,.],.]]]]],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[.,[[[.,.],[.,[[.,.],[.,[[.,.],[.,.]]]]]],[.,.]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[.,[[[.,.],[.,[[[.,.],.],[.,[.,.]]]]],[.,.]]],.]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[.,[.,[[[.,.],.],[.,[[.,.],[.,[[.,.],[.,.]]]]]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[.,[.,[[[.,.],.],[.,[[.,[[[.,.],.],[.,.]]],.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[.,[[[.,.],.],[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[.,[[[.,.],.],[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[.,[[[.,.],.],[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]]]
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[.,[[.,.],[.,[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]]]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[.,[[.,.],[.,[[[.,.],.],[.,[[[.,.],.],[.,.]]]]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[[[.,.],.],[.,[[[.,.],[.,[.,.]]],[.,.]]]]],.]
[1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[.,[.,[[.,.],[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[.,[.,[[.,.],[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[.,[[.,.],[.,[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[[.,.],[.,[[[.,.],[.,[[.,[.,.]],.]]],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[.,[[.,[[[.,.],.],[.,[[.,.],[.,[[.,.],.]]]]]],.]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[.,[[.,[[[.,.],.],[.,[[.,[[.,.],[.,.]]],.]]]],.]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[.,[.,[[[.,.],.],[.,[[[.,.],.],[.,[[.,.],.]]]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[.,[[.,.],[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]]],.]
[1,0,1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[.,[.,[[.,.],[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]]]]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[.,[[.,[[[.,.],[.,[[.,.],[.,.]]]],[[.,.],.]]],.]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[.,[[.,[[[.,.],[.,[[[.,.],.],[.,.]]]],[.,.]]],.]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[.,[[.,[[[.,.],.],[.,[[[.,.],[.,.]],[.,.]]]]],.]]
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[.,[[.,.],[.,[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]]]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[.,[[.,[[[.,.],[.,[[.,.],[.,[.,.]]]]],[.,.]]],.]]
[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[.,[[.,.],[.,[[[.,.],[.,[[.,.],.]]],[[.,.],.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[.,[[.,.],[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]]],.]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[.,[.,[[.,[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]],.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,[[.,.],[.,[[[.,.],[.,.]],[[.,.],.]]]]],.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]],.]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[[[.,.],[.,[[.,[[.,[[.,.],.]],.]],.]]],.]],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],[[.,.],[.,[[.,[[.,[[.,.],.]],.]],.]]]],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[.,[[.,[[.,[[.,.],.]],.]],.]]],.]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[.,[[.,[[[.,.],[.,[[.,[[.,.],.]],.]]],.]],.]],.]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],[.,[[[.,.],[.,[[.,[[.,.],.]],.]]],.]]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[.,[[[.,.],[[.,.],[.,[[.,[[.,.],.]],.]]]],.]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],[[.,.],[[.,.],[.,[[.,[[.,.],.]],.]]]]],.]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[[.,.],[.,[[.,[[.,.],.]],.]]]],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[[.,[[[.,[[.,.],.]],[.,[[.,[[.,.],.]],.]]],.]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],[[.,[[.,.],.]],[.,[[.,[[.,.],.]],.]]]],.]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,[[.,.],.]],.]],[.,[[.,[[.,.],.]],.]]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[[.,.],[.,[[.,[[.,.],.]],.]]],.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,[[.,[[[.,.],[.,[[.,.],.]]],.]],.]],.]],.]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[[.,[[[.,.],[.,[[.,.],.]]],.]],.]]],.]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[.,.],[.,[[[.,.],[.,[[.,.],.]]],.]]],.]],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],[.,[[[.,.],[.,[[.,.],.]]],.]]]],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[.,[[[.,.],[.,[[.,.],.]]],.]]],.]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,[[[.,.],[[.,.],[.,[[.,.],.]]]],.]],.]],.]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[[[.,.],[[.,.],[.,[[.,.],.]]]],.]]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[.,.],[[.,.],[[.,.],[.,[[.,.],.]]]]],.]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],[[.,.],[[.,.],[.,[[.,.],.]]]]]],.]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[[.,.],[[.,.],[.,[[.,.],.]]]]],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[.,[[.,.],.]],[[.,.],[.,[[.,.],.]]]],.]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,[[.,.],.]],[[.,.],[.,[[.,.],.]]]]],.]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,[[.,[[.,.],.]],.]],[[.,.],[.,[[.,.],.]]]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,[[[.,.],[[.,.],[.,[[.,.],.]]]],.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[[.,[[[.,[[.,.],.]],[.,[[.,.],.]]],.]],.]],.]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[[[.,[[.,.],.]],[.,[[.,.],.]]],.]]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[[[.,.],[[.,[[.,.],.]],[.,[[.,.],.]]]],.]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],[[.,[[.,.],.]],[.,[[.,.],.]]]]],.]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[[.,[[.,.],.]],[.,[[.,.],.]]]],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[[[.,[[.,[[.,.],.]],.]],[.,[[.,.],.]]],.]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],[[.,[[.,[[.,.],.]],.]],[.,[[.,.],.]]]],.]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,[[.,.],.]]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0]=>[[[.,[[[.,[[.,.],.]],[.,[[.,.],.]]],.]],[.,.]],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[[.,[[[.,[[[.,.],[.,[[.,.],.]]],.]],[.,.]],.]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[[[.,.],[[.,[[[.,.],[.,[[.,.],.]]],.]],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[[[.,[[.,[[[.,.],[.,[[.,.],.]]],.]],.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,1,1,0,0]=>[[[.,[[[[.,.],[.,[[.,.],.]]],[.,.]],.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[[[.,[[[.,.],[.,[[.,.],.]]],.]],[.,[[.,.],.]]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.]],.]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]]],.]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[[[.,.],[.,[[.,[[[.,.],[.,.]],.]],.]]],.]],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[[.,.],[.,[[.,[[[.,.],[.,.]],.]],.]]]],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,[[.,.],.]],[.,[[.,[[[.,.],[.,.]],.]],.]]],.]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,[[[.,.],[.,[[[.,.],[.,.]],.]]],.]],.]],.]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[.,[[[.,.],[.,[[[.,.],[.,.]],.]]],.]]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[[[.,.],[[.,.],[.,[[[.,.],[.,.]],.]]]],.]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[[.,.],[[.,.],[.,[[[.,.],[.,.]],.]]]]],.]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[[.,[[.,.],.]],[[.,.],[.,[[[.,.],[.,.]],.]]]],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[[[.,[[.,.],.]],[.,[[[.,.],[.,.]],.]]],.]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[[.,[[.,.],.]],[.,[[[.,.],[.,.]],.]]]],.]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[[[.,[[.,[[.,.],.]],.]],[.,[[[.,.],[.,.]],.]]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,1,1,0,0,0]=>[[[.,[[[.,.],[.,[[[.,.],[.,.]],.]]],.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[[.,[[.,[[[.,.],[[.,.],[.,.]]],.]],.]],.]],.]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[[.,.],[.,[[.,[[[.,.],[[.,.],[.,.]]],.]],.]]],.]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[[[.,.],[.,[[[.,.],[[.,.],[.,.]]],.]]],.]],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[[.,.],[[.,.],[.,[[[.,.],[[.,.],[.,.]]],.]]]],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[[.,[[.,.],.]],[.,[[[.,.],[[.,.],[.,.]]],.]]],.]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,[[.,[[[.,.],[[.,.],[[.,.],[.,.]]]],.]],.]],.]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[[.,.],[.,[[[.,.],[[.,.],[[.,.],[.,.]]]],.]]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.]],.]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],[.,.]]]]],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[[.,[[[.,[[.,.],.]],[[.,.],[[.,.],[.,.]]]],.]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],[.,.]]]]],.]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0]=>[[[.,[[[.,.],[[.,.],[[.,.],[.,.]]]],.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[.,[[.,[[[.,[[.,.],.]],[[.,.],[.,.]]],.]],.]],.]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[[.,.],[.,[[[.,[[.,.],.]],[[.,.],[.,.]]],.]]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[.,[[[.,.],[[.,[[.,.],.]],[[.,.],[.,.]]]],.]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],[.,.]]]]],.]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],[.,.]]]],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[[.,[[[.,[[.,[[.,.],.]],.]],[[.,.],[.,.]]],.]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0]=>[[[.,[[[.,[[.,.],.]],[[.,.],[.,.]]],.]],[.,.]],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[[.,[[[.,[[[.,.],[[.,.],[.,.]]],.]],[.,.]],.]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[[[.,.],[[.,[[[.,.],[[.,.],[.,.]]],.]],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[[[.,[[.,[[[.,.],[[.,.],[.,.]]],.]],.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0]=>[[[.,[[[[.,.],[[.,.],[.,.]]],[.,.]],.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0,0]=>[[[.,[[[.,.],[[.,.],[.,.]]],.]],[.,[[.,.],.]]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[[.,[[.,[[[.,[[.,.],.]],[.,.]],.]],.]],.]],.]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[[.,.],[.,[[.,[[[.,[[.,.],.]],[.,.]],.]],.]]],.]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[[[.,.],[.,[[[.,[[.,.],.]],[.,.]],.]]],.]],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[[.,.],[[.,.],[.,[[[.,[[.,.],.]],[.,.]],.]]]],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[[.,[[.,.],.]],[.,[[[.,[[.,.],.]],[.,.]],.]]],.]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[.,[[.,[[[.,.],[[.,[[.,.],.]],[.,.]]],.]],.]],.]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[.,.],[.,[[[.,.],[[.,[[.,.],.]],[.,.]]],.]]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[.,[[[.,.],[[.,.],[[.,[[.,.],.]],[.,.]]]],.]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],[.,.]]]]],.]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],[.,.]]]],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[[.,[[[.,[[.,.],.]],[[.,[[.,.],.]],[.,.]]],.]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],[.,.]]]],.]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0,0]=>[[[.,[[[.,.],[[.,[[.,.],.]],[.,.]]],.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[.,[[.,[[[.,[[.,[[.,.],.]],.]],[.,.]],.]],.]],.]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[[.,.],[.,[[[.,[[.,[[.,.],.]],.]],[.,.]],.]]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[.,[[[.,.],[[.,[[.,[[.,.],.]],.]],[.,.]]],.]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],[.,.]]]],.]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],[.,.]]],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[[.,[[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,.]],.]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0]=>[[[.,[[[.,[[.,[[.,.],.]],.]],[.,.]],.]],[.,.]],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[[.,[[[.,[[[.,[[.,.],.]],[.,.]],.]],[.,.]],.]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[[[.,.],[[.,[[[.,[[.,.],.]],[.,.]],.]],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[[[.,[[.,[[[.,[[.,.],.]],[.,.]],.]],.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0,0]=>[[[.,[[[[.,[[.,.],.]],[.,.]],[.,.]],.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0,0]=>[[[.,[[[.,[[.,.],.]],[.,.]],.]],[.,[[.,.],.]]],.]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[.,[[.,[[[.,[[[.,.],[.,.]],.]],[.,.]],.]],.]],.]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[[.,.],[.,[[[.,[[[.,.],[.,.]],.]],[.,.]],.]]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[.,[[[.,.],[[.,[[[.,.],[.,.]],.]],[.,.]]],.]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[[.,.],[[.,.],[[.,[[[.,.],[.,.]],.]],[.,.]]]],.]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[[.,[[.,.],.]],[[.,[[[.,.],[.,.]],.]],[.,.]]],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[[.,[[[.,[[.,[[[.,.],[.,.]],.]],.]],[.,.]],.]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[[[.,.],[[.,[[.,[[[.,.],[.,.]],.]],.]],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0,0]=>[[[.,[[[.,[[[.,.],[.,.]],.]],[.,.]],.]],[.,.]],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[[.,[[[.,[[[[.,.],[.,.]],[.,.]],.]],[.,.]],.]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[[[.,.],[[.,[[[[.,.],[.,.]],[.,.]],.]],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[[[.,[[.,[[[[.,.],[.,.]],[.,.]],.]],.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[[[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,0]=>[[[.,[[[[.,.],[.,.]],[.,.]],.]],[.,[[.,.],.]]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[[.,.],[[.,[[[.,.],[.,.]],.]],[.,[[.,.],.]]]],.]
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[[.,[[.,[[[.,.],[.,.]],.]],.]],[.,[[.,.],.]]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0]=>[[[.,[[[[.,.],[.,.]],[.,[[.,.],.]]],.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[[[.,[[[.,.],[.,.]],.]],[.,[[.,[[.,.],.]],.]]],.]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[.,[[[[.,[.,.]],.],.],[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[[.,[.,.]],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.],.]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[.,[[.,[.,.]],[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[.,[[[.,[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[.,[[[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[.,[.,[.,[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[.,[[.,[.,.]],[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[.,[[[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]],.],.]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[.,[[[.,[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]],.],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[.,[.,[.,[.,[[[.,[[[.,[.,[.,.]]],.],.]],.],.]]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[.,[[[.,[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[.,[.,[.,[.,[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[.,[.,[.,[.,[.,[[[.,[[[.,[.,.]],.],.]],.],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[.,[.,[.,[.,[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[.,[.,[.,[.,[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[.,[.,[.,[.,[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[.,[[.,[[[.,.],.],.]],[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[.,[[[.,[.,.]],[.,[[[.,[.,[.,[.,.]]]],.],.]]],.]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[.,[.,[[[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]],.],.]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[.,[.,[[[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]],.],.]]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[.,[[[[[.,[.,.]],.],.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[[.,[.,.]],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[.,[.,[[[[.,[.,.]],.],.],[[.,[.,[.,[.,.]]]],.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[.,[.,[[.,[.,.]],[[.,[[[.,[.,[.,.]]],.],.]],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[.,[.,[[[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]],.],.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[.,[.,[[.,[.,.]],[[.,[.,.]],[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[.,[.,[[[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]],.],.]]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[.,[.,[[[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]],.],.]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[.,[.,[[[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]],.],.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[.,[[[.,[[[.,.],.],.]],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]]]]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[.,[.,[[.,[[[.,.],.],.]],[[.,[.,[.,[.,.]]]],.]]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[.,[.,[[[.,[.,.]],[.,[[[.,[.,[.,.]]],.],.]]],.]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[.,[.,[.,[[[.,[.,[[[.,[.,[.,.]]],.],.]]],.],.]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[.,[.,[.,[[[.,[.,[.,[[[.,[.,.]],.],.]]]],.],.]]]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[.,[.,[[[[[.,[.,.]],.],.],[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]]]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[.,[.,[.,[[[[.,[.,.]],.],.],[[.,[.,[.,.]]],.]]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[.,[.,[.,[[.,[.,.]],[[.,[[[.,[.,.]],.],.]],.]]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[.,[.,[.,[[.,[.,.]],[[.,[.,.]],[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[.,[.,[.,[[[.,[[.,[.,.]],[[.,[.,.]],.]]],.],.]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[.,[.,[.,[[[.,[[[.,[.,.]],[.,[.,.]]],.]],.],.]]]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[.,[.,[[[.,[[[.,.],.],.]],[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]]]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[.,[.,[.,[[.,[[[.,.],.],.]],[[.,[.,[.,.]]],.]]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[.,[.,[.,[[[.,[.,.]],[.,[[[.,[.,.]],.],.]]],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[.,[.,[.,[[[[[.,[.,.]],.],.],[.,[.,[.,.]]]],.]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[.,[.,[.,[.,[[[[.,[.,.]],.],.],[[.,[.,.]],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[.,[.,[.,[.,[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[.,[.,[.,[[[.,[[[.,.],.],.]],[.,[.,[.,.]]]],.]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[.,[.,[.,[.,[[.,[[[.,.],.],.]],[[.,[.,.]],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[.,[.,[.,[.,[[[[[.,[.,.]],.],.],[.,[.,.]]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[.,[.,[.,[.,[[[.,[[[.,.],.],.]],[.,[.,.]]],.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[[[[.,[.,.]],.],[[.,[.,.]],[[.,.],.]]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,[.,.]],.],.],[[.,[[.,[[[.,.],.],.]],.]],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[[.,[[[.,.],.],.]],.],[[[.,.],.],.]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],.],.],[[[[.,[.,.]],.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[.,[[.,[.,.]],[.,[[[.,.],.],.]]]],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[[.,[.,.]],.],.],[[.,[[[.,.],.],.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,[[.,[.,.]],[[.,.],.]]],.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[.,[[.,[[.,[[[.,.],.],.]],.]],.]],.]]
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0]=>[[[[.,[.,.]],[[[.,.],.],.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[[[[.,[[[.,.],.],.]],.],.],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[.,[.,.]],[.,[[.,[[[.,.],.],.]],.]]]]
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]=>[[[[.,[[[.,.],.],[[[.,.],.],.]]],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[[.,[.,.]],.],[[.,.],.]],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,[[[[.,[.,.]],.],.],[.,[[[.,.],.],.]]]],.],.]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[.,.]],[[[[.,[[[.,.],.],.]],.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],[.,[[.,[.,.]],[[.,.],.]]]]],.],.]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[[.,[.,.]],[.,[[.,[[[.,.],.],.]],.]]]],.],.]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[[[[.,[[[.,.],[[[.,.],.],.]],.]],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[[.,[.,.]],[[.,.],.]],.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[.,[[.,[[[.,.],.],.]],[.,[[[.,.],.],.]]]],.],.]
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[[[.,.],.],[[.,.],.]]],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[.,[[.,[[[[.,[.,.]],.],.],[[.,.],.]]],.]],.],.]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,[[.,[[.,[.,.]],[.,[[[.,.],.],.]]]],.]],.],.]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[[[.,.],[[.,.],.]],.]],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,[[.,[[.,[[[.,.],.],.]],[[.,.],.]]],.]],.],.]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,[[.,[[.,[[.,[.,.]],[[.,.],.]]],.]],.]],.],.]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[[.,[[.,[[.,[[[.,.],.],.]],.]],.]],.]],.],.]
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[[[[.,[.,.]],.],[[[.,.],.],.]],[.,[[[.,.],.],.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[[.,[.,.]],[[.,.],.]]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[.,[[[.,.],.],.]],[[.,[[.,[[[.,.],.],.]],.]],.]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[[.,[[[.,.],.],.]],[[[.,.],.],.]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,[[[.,.],.],.]],[[[[.,[.,.]],.],.],[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]],.]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[[[.,.],.],.]],[[.,[[[.,.],.],.]],[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,[.,.]],[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]],.]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[.,[[.,[[.,[[[.,.],.],.]],.]],.]]],.]
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,1,0,0]=>[[[[.,[.,.]],[[[.,.],.],.]],.],[[[.,[.,.]],.],.]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[[.,[[[.,.],.],[[.,[.,.]],[[.,.],.]]]],[.,[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[[.,[.,.]],.],.],[.,[[.,[[[.,.],.],.]],.]]],.]
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,1,0,0]=>[[.,[[[.,.],.],[[[.,.],.],.]]],[[[.,[.,.]],.],.]]
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[.,[.,.]],.],[[.,.],.]],[[[.,[.,.]],.],.]],.]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[.,[[[[.,[.,.]],.],[.,[[[.,.],.],.]]],[.,[.,.]]]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[[[.,[[[.,.],.],.]],.],[[.,.],.]],[.,[.,.]]],.]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],.],.],[.,[[.,[.,.]],[[.,.],.]]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[.,[[[[.,[.,.]],.],.],[.,[[.,[[[.,.],.],.]],.]]]]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[[.,[[[.,.],[[[.,.],.],.]],[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[[[[.,[.,.]],[[.,.],.]],[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[.,[[[[.,[[[.,.],.],.]],.],.],[.,[[[.,.],.],.]]]]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[[[.,[[[.,.],.],[[.,.],.]]],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[.,.]],[.,[[[[.,[.,.]],.],.],[[.,.],.]]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[.,[[.,[.,.]],[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[[[.,[[[.,.],[[.,.],.]],.]],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[.,[.,.]],[.,[[.,[[[.,.],.],.]],[[.,.],.]]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[.,[[.,[.,.]],[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[.,[[.,[.,.]],[.,[[.,[[.,[[[.,.],.],.]],.]],.]]]]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0,0]=>[[[[.,[.,.]],[[[.,.],.],.]],.],[.,[[[.,.],.],.]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,0,0]=>[[.,[[[.,.],[[.,[.,.]],[[.,.],.]]],.]],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[[[.,.],.],.]],[.,[[.,[[[.,.],.],.]],.]]],.]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,1,0,0]=>[[.,[[[.,.],.],[[[.,.],.],.]]],[.,[[[.,.],.],.]]]
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[.,[.,.]],.],[[.,.],.]],[.,[[[.,.],.],.]]],.]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[.,[[[[.,[.,.]],[.,[[[.,.],.],.]]],.],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[[[.,[[[.,.],.],.]],[[.,.],.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[.,[[.,[[[.,.],.],.]],[.,[[.,[.,.]],[[.,.],.]]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[.,[[.,[[[.,.],.],.]],[.,[[.,[[[.,.],.],.]],.]]]]
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,1,0,0]=>[[.,[[[.,.],[[[.,.],.],.]],.]],[[[.,[.,.]],.],.]]
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[[[[[.,[.,.]],[[.,.],.]],.],[[[.,[.,.]],.],.]],.]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[.,[[.,[[[.,.],.],[.,[[[.,.],.],.]]]],[.,[.,.]]]]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[[[.,[[[.,.],.],[[.,.],.]]],[[[.,[.,.]],.],.]],.]
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,[.,.]],.],[[.,.],.]],[.,[.,.]]]],.]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[.,[[.,[[[[.,[.,.]],.],.],[.,[[[.,.],.],.]]]],.]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[.,[[[.,.],[[.,.],.]],[.,[.,.]]]],[.,[.,.]]],.]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[.,[[[[.,[[[.,.],.],.]],.],.],[[.,.],.]]],.]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[.,[[.,[[.,[.,.]],[.,[[.,[.,.]],[[.,.],.]]]]],.]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[.,[[.,[[.,[.,.]],[.,[[.,[[[.,.],.],.]],.]]]],.]]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,0,0]=>[[.,[[[.,.],[[[.,.],.],.]],.]],[.,[[[.,.],.],.]]]
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[[[[[.,[.,.]],[[.,.],.]],.],[.,[[[.,.],.],.]]],.]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[.,[[.,[[[.,.],[.,[[[.,.],.],.]]],.]],[.,[.,.]]]]
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[[[.,[[[.,.],.],[[.,.],.]]],[.,[[[.,.],.],.]]],.]
[1,0,1,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,[.,.]],[[.,.],.]],.],[.,[.,.]]]],.]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[.,[[.,[[.,[[[.,.],.],.]],[.,[[[.,.],.],.]]]],.]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>[[[.,[[[.,.],[[.,.],.]],.]],[[[.,[.,.]],.],.]],.]
[1,0,1,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,[[[.,.],.],[[.,.],.]]],[.,[.,.]]]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[[[.,[.,.]],.],.],[[.,.],.]]],.]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[.,[[.,[[.,[[.,[.,.]],[.,[[[.,.],.],.]]]],.]],.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[[[.,[[[.,.],[[.,.],.]],.]],[.,[[[.,.],.],.]]],.]
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[[.,[[[.,.],[[.,.],.]],.]],[.,[.,.]]]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,[[.,[[[.,.],.],.]],[[.,.],.]]],.]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,[[.,[.,.]],[[.,.],.]]],.]],.]],.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[[[.,[[[.,.],[.,.]],.]],[.,[[.,.],[[.,.],.]]]],.]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]=>[[[.,[[[.,.],[[.,.],[.,.]]],.]],[[[.,.],.],.]],.]
[1,1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[[[.,[[[.,.],[.,.]],.]],[[.,[.,.]],[[.,.],.]]],.]
[1,1,0,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,0,0]=>[[[.,[[.,[[.,.],.]],[.,.]]],[.,[.,[[.,.],.]]]],.]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0,0]=>[[[.,[[.,.],[[[.,.],.],[[.,.],.]]]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0,0,0]=>[[[.,[[.,[.,[[.,.],.]]],[.,.]]],[.,[[.,.],.]]],.]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,[[.,.],[[.,[[[.,.],.],.]],[.,.]]]],[.,.]],.]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[[[.,[[.,.],[[[[.,.],.],.],[[.,.],.]]]],[.,.]],.]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,1,1,0,0,0]=>[[[.,[[.,[.,.]],[[.,.],[.,.]]]],[[[.,.],.],.]],.]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[[[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]],[[.,.],.]],.]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,0,0]=>[[[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]],[[.,.],.]],.]
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,[[.,.],[.,.]]],[[[.,[.,.]],.],[[.,.],.]]],.]
[1,1,0,1,1,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,0]=>[[[[[[[.,.],[.,.]],[.,.]],.],.],[.,[[.,.],.]]],.]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0,0,1,0,0]=>[[[[[[.,[[.,.],[[.,.],.]]],[.,.]],.],.],[.,.]],.]
[1,1,0,1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0,1,1,0,0,0]=>[[[[[[[.,.],.],[[.,.],[.,.]]],.],.],[[.,.],.]],.]
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[[[[.,.],.],.],[[[.,.],.],[[.,[.,.]],[.,.]]]],.]
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[[[[.,.],.],.],[[[.,[.,.]],[[.,.],.]],[.,.]]],.]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,0,0]=>[[[[[.,[[[.,.],[.,.]],.]],[.,.]],.],[.,[.,.]]],.]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[[[.,[.,[[.,.],[[.,.],.]]]],[.,.]],.],[.,.]],.]
[1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[[[[[.,[[[[.,.],[.,.]],.],.]],[.,.]],.],[.,.]],.]
[1,1,0,1,1,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[[.,.],.],[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]],.]
[1,1,0,1,1,1,0,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[[[[.,.],.],[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]],.]
[1,1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,1,1,0,0,0]=>[[[[[[[.,.],.],.],[[.,.],[.,.]]],.],[[.,.],.]],.]
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[[[[.,.],.],[[[[[.,[.,.]],[.,.]],.],.],[.,.]]],.]
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[[[[.,.],.],[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]],.]
[1,1,0,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[[[.,.],.],[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]],.]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0,0,0]=>[[[[.,[[.,[[.,.],.]],.]],[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[[.,[.,.]],[[[.,.],.],[[.,.],.]]],[.,[.,.]]],.]
[1,1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[[.,[[[.,[[.,.],.]],.],.]],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[[.,[.,[[[[.,.],.],[.,.]],.]]],[.,.]],[.,.]],.]
[1,1,0,1,1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[[.,[.,[[[.,.],.],[[.,.],.]]]],[.,.]],[.,.]],.]
[1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0,0]=>[[[[[.,[.,[[.,.],.]]],.],[.,.]],[.,[[.,.],.]]],.]
[1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[[.,[[[.,[[[.,.],.],.]],.],.]],[.,.]],[.,.]],.]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[[[[.,[[.,[[[[.,.],.],.],.]],.]],[.,.]],[.,.]],.]
[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[[[[.,[[[[.,.],.],.],[[.,.],.]]],[.,.]],[.,.]],.]
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,0,0]=>[[[[[.,[.,.]],.],[[.,.],[.,.]]],[[[.,.],.],.]],.]
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[[[[[[.,[[.,[.,.]],.]],.],.],[.,.]],[[.,.],.]],.]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[[[[[.,[[[.,[.,.]],.],.]],.],[.,.]],[[.,.],.]],.]
[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[[[[[[.,[.,[.,.]]],.],[.,.]],[.,.]],[[.,.],.]],.]
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[.,.],[.,[.,.]]],[[[.,[.,.]],.],[[.,.],.]]],.]
[1,1,1,0,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[[.,[.,[[[.,.],[.,.]],.]]],[.,[[.,[[.,.],.]],.]]]
[1,1,1,0,1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0,1,0,0]=>[[.,[.,[[[[.,.],[[.,.],.]],[[.,.],.]],.]]],[.,.]]
[1,1,1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0]=>[[.,[.,[[[.,.],[[.,.],[.,.]]],.]]],[[.,[.,.]],.]]
[1,1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[[.,[.,[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]]],[.,.]]
[1,1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[[.,[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]],[[.,.],.]]
[1,1,1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0,0]=>[[.,[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[[.,[.,[[[.,.],.],[[[.,.],.],[[.,.],.]]]]],[.,.]]
[1,1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[[.,[.,[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]]],[.,.]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[[[.,.],.],[[.,[[[.,.],.],.]],[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],.],[[[[.,.],.],.],[[.,.],.]]]]
[1,1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0,0]=>[[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[[[.,[.,[[.,[.,.]],.]]],[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0,0]=>[[.,[.,.]],[[[.,[[.,[.,[.,.]]],.]],[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[[.,[.,.]],.],[[.,.],.]],[[.,.],.]]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0]=>[[.,[[[[[.,.],[.,.]],[.,[[.,.],.]]],.],.]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[[.,[[[.,[[[.,.],[[.,.],.]],.]],.],.]],[[.,.],.]]
[1,1,1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[[.,[[[.,[[.,.],[[.,.],[.,.]]]],.],.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[[.,[[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]],.]],[.,.]]
[1,1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[[.,[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]],[[.,.],.]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[.,[[[[[.,.],[.,.]],.],[.,[[.,.],.]]],.]],[.,.]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[[.,[[.,[[[[.,.],[[.,.],.]],.],.]],.]],[[.,.],.]]
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[[.,[[.,[[[.,.],[.,.]],.]],.]],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[.,.],[[.,[[[.,.],[.,.]],.]],[.,[[[.,.],.],.]]]]
[1,1,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[[.,.],[[.,[[[.,.],[[.,.],.]],.]],[[[.,.],.],.]]]
[1,1,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0,0]=>[[.,[[.,[[.,.],[[.,.],[.,.]]]],.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0,0]=>[[.,.],[[.,[[.,[.,.]],[.,.]]],[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0]=>[[.,.],[[.,[[.,[.,[.,.]]],[.,.]]],[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[.,.]],[[.,.],.]]],[[[.,.],.],.]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[[.,[[[[.,[[.,.],.]],[.,.]],.],[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[[.,[[[[.,.],.],.],[[[.,.],.],[[.,.],.]]]],[.,.]]
[1,1,1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[[.,[[[[.,[[.,.],.]],[.,.]],.],[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[[.,.],[[[[[[.,.],.],[.,.]],.],.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[[.,.],[[[[[[.,.],.],[[.,.],.]],.],.],[[.,.],.]]]
[1,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,1,0,0,0,0]=>[[.,[[[.,[.,[[.,.],.]]],[.,.]],[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[[.,.],[[[[.,[[[.,.],.],.]],[.,.]],.],[.,[.,.]]]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,0,0]=>[[.,.],[[[[.,[[[[.,.],.],.],.]],[.,.]],.],[.,.]]]
[1,1,1,0,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,1,0,0]=>[[.,.],[[[[[[.,.],.],.],[[.,.],.]],.],[[.,.],.]]]
[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0,1,1,0,0,0]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],[[.,[.,[.,.]]],.]]
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,0,0]=>[[.,.],[[[.,[[.,[.,.]],.]],[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0,0]=>[[.,.],[[[.,[[[.,[.,.]],.],.]],[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0,0,0]=>[[.,.],[[[[.,[.,[.,.]]],.],[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[[.,[.,.]],.],[[.,.],.]],[[[.,.],.],.]]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[[[[[[[[.,.],[.,.]],[.,.]],[.,.]],.],.],.],[.,.]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[[[[[.,[[.,[[.,.],[[.,.],.]]],.]],.],.],.],[.,.]]
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[[[[[.,[[[.,.],.],[[.,.],[.,.]]]],.],.],.],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[[[.,[.,.]],.],.],[[[.,.],.],[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],.],.],[[[.,[.,.]],[[.,.],.]],[.,.]]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[[[[[[[[.,.],[.,.]],[.,.]],.],[.,.]],.],.],[.,.]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[[[[.,[[[.,[[.,.],[[.,.],.]]],.],.]],.],.],[.,.]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[[[[.,[[[[.,.],[.,.]],[.,.]],.]],.],.],[.,[.,.]]]
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[[[.,[.,[[[.,.],[.,.]],.]]],.],[.,[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[[[.,[.,[[[.,.],[[.,.],.]],.]]],.],[[.,[.,.]],.]]
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0]=>[[[[.,[[[.,.],.],[[.,.],[.,.]]]],.],.],[.,[.,.]]]
[1,1,1,1,0,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0]=>[[[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]],.],[.,[.,.]]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0,0]=>[[[.,[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]],.],[.,.]]
[1,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[[[.,[.,[[.,[.,.]],[[.,.],.]]]],.],[[.,[.,.]],.]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[[[[[.,[[[.,.],[.,.]],.]],.],[.,.]],.],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[[[.,[.,[[.,.],[[.,.],.]]]],.],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[[[[[[[[.,.],[.,.]],.],[.,.]],.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[[[.,[[[[[.,.],[.,.]],[.,[.,.]]],.],.]],.],[.,.]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[[[.,[[[.,[[.,.],[[.,.],.]]],.],.]],.],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0]=>[[[[[[[[.,.],[.,.]],.],.],[.,.]],[.,.]],.],[.,.]]
[1,1,1,1,0,0,1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0,0,0]=>[[[.,[[[[[.,.],[.,.]],.],[.,[.,.]]],.]],.],[.,.]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[[[.,[[.,[[[.,.],[.,.]],.]],.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[[[.,[[.,[[.,.],[[.,.],.]]],.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0,0,1,1,0,0,0]=>[[[[[[.,.],.],.],[[.,.],[.,.]]],.],[[.,[.,.]],.]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0,0,0]=>[[[.,[[[[.,[.,.]],[.,.]],.],[.,.]]],.],[.,[.,.]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[[[.,[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]],.],[.,.]]
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[[[.,[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]],.],[.,.]]
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],[[.,.],.]]],.],[[.,[.,[.,.]]],.]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[[[[.,[[.,[[.,.],.]],.]],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[[.,[.,.]],.],[[[.,.],.],[[.,.],.]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[[[[[[.,[[.,.],.]],.],[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[[[[[[[[.,.],.],[.,.]],[.,.]],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[[[.,[[[.,.],.],[[.,.],.]]],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0,1,1,0,0,0,0]=>[[[[[[.,[[.,.],.]],.],.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0,0]=>[[[[[[[[.,.],.],[.,.]],.],[.,.]],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[[[[.,[[[[.,.],.],[.,.]],.]],.],[.,[.,.]]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[[.,[[[.,.],.],[[.,.],.]]],.],[.,[.,.]]],[.,.]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,1,1,0,0,0,0]=>[[[[.,[.,[[.,.],.]]],.],[.,.]],[.,[[.,[.,.]],.]]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[[[.,[[[.,.],.],.]],.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[[[[[[[[.,.],.],.],[.,.]],.],[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[[[[[[[[.,.],.],.],.],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0,0,0,1,0,0]=>[[[[[[.,.],.],.],[[.,.],.]],[[.,[.,.]],.]],[.,.]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0]=>[[[[.,[.,.]],.],[[.,.],[.,.]]],[[[.,[.,.]],.],.]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0,0]=>[[[[.,[[.,[.,.]],.]],.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[[[[[[.,[.,.]],.],[.,.]],.],[.,.]],[[.,[.,.]],.]]
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[[[[[[.,[.,.]],.],.],[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,0]=>[[[[.,[.,[.,.]]],.],[.,.]],[[.,[[.,[.,.]],.]],.]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[.,[[[.,[.,[[.,[.,.]],.]]],[[.,[.,.]],.]],[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[.,[[[[.,.],.],[[[.,.],[[.,[.,.]],.]],.]],[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[.,[[[.,.],.],[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[.,[[[.,.],.],[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[.,[[[[.,[.,.]],.],[.,[.,[[.,[.,.]],.]]]],[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[.,[[[.,.],.],[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[.,[[.,.],[[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]],.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[.,[[[.,[.,.]],.],[[[[.,.],.],[[.,[.,.]],.]],.]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[.,[[.,[.,[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]]],.]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[.,[[[.,.],[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[[[.,[.,.]],.],[[[[.,.],.],[[.,.],.]],.]],.]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[.,[[.,[[.,[.,.]],.]],[[[[.,.],.],[.,[.,.]]],.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[.,[[[.,[[.,[.,.]],.]],[[[[.,.],.],[.,.]],.]],.]]
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[.,[[[[.,[.,.]],.],[[.,.],.]],[.,.]]]],.]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[.,[[.,[.,[[[.,.],.],[[[.,.],[[.,.],.]],.]]]],.]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[.,[[.,[.,[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]]],.]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[.,[[[.,.],[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]],.]]
[1,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[.,[[.,.],[[[[[.,[.,.]],.],[.,[.,.]]],[.,.]],.]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[.,[[.,.],[[[[.,.],.],[[[.,.],[.,[.,.]]],.]],.]]]
[1,0,1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[.,[[[.,[.,[[[.,.],.],[[.,[.,.]],.]]]],.],[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[.,[[[[[.,[.,.]],[[.,[.,.]],.]],.],[.,.]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[.,[[[.,[.,[[.,.],.]]],.],[.,[.,[[.,[.,.]],.]]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,[.,[[.,.],[[[[.,[.,.]],.],[.,.]],.]]]],.]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[.,[[.,[.,[[[.,[.,[[.,.],.]]],.],[[.,.],.]]]],.]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[.,[[.,.],[[[[.,[.,[[.,.],.]]],.],[.,[.,.]]],.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[.,[[[.,.],[[[[.,[.,[[.,.],.]]],.],[.,.]],.]],.]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[.,[[[.,.],[[[[[.,[.,.]],.],[.,.]],[.,.]],.]],.]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,.],[[[[.,.],.],[[[.,.],[.,.]],.]],.]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[[[.,[.,[[[.,.],.],[[.,.],.]]]],.],[.,.]],.]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[[[[[.,[.,.]],[[.,.],.]],.],[.,.]],[.,.]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[.,[[[[.,[.,[[.,.],.]]],.],[.,[.,[[.,.],.]]]],.]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[.,[[.,[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]],[.,.]]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[.,[[.,[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[.,[[[[[[.,.],[[.,[.,.]],.]],.],[.,.]],.],[.,.]]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[.,[[.,[.,[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]]],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[.,[[[.,[[.,[.,[[[.,.],.],[.,.]]]],.]],[.,.]],.]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[[.,[[[[.,[.,.]],[.,.]],.],[.,.]]],[.,.]],.]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0]=>[.,[[[[[[[.,.],[[.,.],.]],.],[.,.]],.],[.,.]],.]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0]=>[.,[[.,[[[[[.,.],[.,[.,.]]],.],[.,.]],.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[.,[[[.,[[[[[.,.],[.,.]],.],[.,.]],.]],[.,.]],.]]
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[[[.,[.,.]],.],[[.,.],.]],[[.,[.,.]],.]],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,[.,[[.,[.,.]],.]]],[[.,.],.]],[.,.]],.]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[.,.],.],[[[.,.],[[.,.],.]],.]],[.,.]],.]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[.,[[[[.,.],.],[[.,[.,[[.,.],[[.,.],.]]]],.]],.]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[.,[[[[.,.],.],[.,[.,[[[.,.],[[.,.],.]],.]]]],.]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[.,[[[[[.,[.,.]],.],[.,[.,[[.,.],.]]]],[.,.]],.]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[.,[[[[.,.],.],[[[.,.],[.,[.,[[.,.],.]]]],.]],.]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[.,[[.,.],[.,[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[.,[[[.,.],.],[[[.,[[.,.],.]],[[.,[.,.]],.]],.]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[.,[[.,[.,[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]]],.]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,.],[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]],.]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[[[.,.],.],[[[.,[[.,.],.]],[[.,.],.]],.]],.]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[.,[[.,[[.,.],.]],[[[.,[[.,.],.]],[.,[.,.]]],.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,[[.,.],.]],[[[.,[[.,.],.]],[.,.]],.]],.]]
[1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[.,[[.,[[[.,[.,.]],.],[.,[.,.]]]],[[.,[.,.]],.]]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[.,[[.,[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]],[.,.]]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[.,[[.,[[[.,.],.],[[[.,.],[.,[.,.]]],.]]],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[.,[[.,[[.,.],.]],[[.,[.,[[.,.],[.,[.,.]]]]],.]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[.,[[.,[[.,.],.]],[.,[.,[[[.,.],[.,[.,.]]],.]]]]]
[1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[.,[[[[[.,.],.],[[.,[.,.]],.]],.],[[.,[.,.]],.]]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[.,[[[[.,[.,[[.,.],.]]],[[.,[.,.]],.]],.],[.,.]]]
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[.,[[[.,[.,.]],[[.,[.,.]],.]],[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[.,[[[[.,[.,.]],.],[[.,[.,.]],.]],[[[.,.],.],.]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[.,[[[.,.],[[[.,.],[[.,[.,.]],.]],.]],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[.,[[[[[.,.],.],[.,[.,[[.,[.,.]],.]]]],.],[.,.]]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[.,[[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[.,[[.,.],[[.,[.,[[[[.,.],.],.],[.,[.,.]]]]],.]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[.,[[[.,.],[[.,[.,[[[[.,.],.],.],[.,.]]]],.]],.]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[.,[[.,[.,[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]]],.]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[.,[.,[[.,[[.,.],.]],[[[.,.],[.,.]],.]]]],.]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[[[[.,.],.],[[.,.],.]],.],[.,.]]]],.]]
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[.,[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]]],.]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[.,[[.,[.,[[[[.,.],.],.],[.,[.,[[.,.],.]]]]]],.]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[.,[[.,.],[[[[[[.,.],.],[.,[.,.]]],.],[.,.]],.]]]
[1,0,1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[.,[[.,.],[[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]],.]]]
[1,0,1,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[.,[[[.,[.,[[.,.],[[.,[.,.]],.]]]],.],[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[.,[.,[[.,.],[[[[[.,.],.],.],[.,.]],.]]]],.]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[.,[[[.,.],[[[[[[.,.],.],[.,.]],.],[.,.]],.]],.]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[.,[[[.,.],[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[[[.,[.,[[.,.],[[.,.],.]]]],.],[.,[.,.]]],.]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[.,[[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[.,[[[.,[[.,[.,[[.,.],[.,.]]]],.]],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[.,[[[.,[[[.,[.,.]],.],[.,.]]],[[.,[.,.]],.]],.]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[.,[[[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]],[.,.]],.]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[[.,.],.],[[[.,.],[.,.]],.]]],[.,.]],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[.,[[[.,[[.,.],.]],[[.,[.,[[.,.],[.,.]]]],.]],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[.,[[[.,[[.,.],.]],[.,[.,[[[.,.],[.,.]],.]]]],.]]
[1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[[[[[.,.],.],[[.,.],.]],.],[[.,[.,.]],.]],.]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0]=>[.,[[[[[.,[.,[[.,.],.]]],[[.,.],.]],.],[.,.]],.]]
[1,0,1,1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[[.,.],.]],[.,[[.,[.,.]],.]]],.]]
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[[[.,[.,.]],.],[[.,.],.]],[[[.,.],.],.]],.]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[.,.],[[[.,.],[[.,.],.]],.]],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0]=>[.,[[[[[[.,.],.],[.,[.,[[.,.],.]]]],.],[.,.]],.]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,1,1,0,0]=>[.,[[[[.,[.,.]],[.,[.,[[.,.],.]]]],[.,[.,.]]],.]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[.,[[.,.],[.,[.,[[[[[.,.],.],.],[.,[.,.]]],.]]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[[.,.],[.,[.,[[[[[.,.],.],.],[.,.]],.]]]],.]]
[1,0,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0]=>[.,[[.,[[[[.,.],.],[.,[.,.]]],.]],[[.,[.,.]],.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0,1,0]=>[.,[[.,[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]],[.,.]]]
[1,0,1,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0,1,0]=>[.,[[.,[[.,[.,.]],[.,[.,.]]]],[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0]=>[.,[[.,[[[.,[.,.]],.],[.,[.,.]]]],[[[.,.],.],.]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0,1,0]=>[.,[[.,[[.,.],[[[.,.],[.,[.,.]]],.]]],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0,1,0]=>[.,[[[[.,.],[[.,[.,.]],.]],.],[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0]=>[.,[[[[[.,.],.],[[.,[.,.]],.]],.],[[[.,.],.],.]]]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0]=>[.,[[[.,[.,.]],[[.,[.,.]],.]],[.,[[[.,.],.],.]]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[.,[[[[.,.],[.,[.,[[.,[.,.]],.]]]],.],[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[.,[[.,[.,[[.,[[[[.,.],.],[.,.]],.]],[.,.]]]],.]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[.,[[.,[.,[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]]],.]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[[[[.,.],[[.,.],.]],.],[.,[.,.]]]]],.]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[.,[[.,.],[[[[[.,.],[.,[.,.]]],.],[.,[.,.]]],.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[[.,.],[[[[[.,.],[.,.]],.],[.,[.,.]]],.]],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[.,[[[.,[[[[.,.],.],[.,.]],.]],[[.,[.,.]],.]],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[.,[[[.,[[[.,[.,[[.,.],.]]],[.,.]],.]],[.,.]],.]]
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0]=>[.,[[[.,[[.,[.,.]],[.,.]]],[.,[[.,[.,.]],.]]],.]]
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0]=>[.,[[[.,[[[.,[.,.]],.],[.,.]]],[[[.,.],.],.]],.]]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[.,.],[[[.,.],[.,.]],.]]],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0]=>[.,[[[[[.,.],[[.,.],.]],.],[.,[[.,[.,.]],.]]],.]]
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[.,[[[[[[.,.],.],[[.,.],.]],.],[[[.,.],.],.]],.]]
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[[.,.],.]],[.,[[[.,.],.],.]]],.]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0]=>[.,[[[[[.,.],[.,[.,[[.,.],.]]]],.],[.,[.,.]]],.]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0]=>[.,[[.,[[[.,.],[.,[.,.]]],.]],[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>[.,[[.,[[[[.,.],.],[.,[.,.]]],.]],[[[.,.],.],.]]]
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0]=>[.,[[.,[[.,[.,.]],[.,[.,.]]]],[.,[[[.,.],.],.]]]]
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[.,[[[[.,.],[[.,[.,.]],.]],.],[.,[[[.,.],.],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[.,[.,[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]]],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[.,[[[.,[[[.,.],[.,.]],.]],[.,[[.,[.,.]],.]]],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[.,[[[.,[[[[.,.],.],[.,.]],.]],[[[.,.],.],.]],.]]
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>[.,[[[.,[[.,[.,.]],[.,.]]],[.,[[[.,.],.],.]]],.]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[.,[[[[[.,.],[[.,.],.]],.],[.,[[[.,.],.],.]]],.]]
[1,1,1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,1,0,0,0]=>[[.,[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,.],[.,[.,.]]],[.,[[[.,[.,.]],.],[[.,.],.]]]]
[1,1,1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0,1,0,0]=>[[.,[.,[[.,[.,.]],[[.,.],.]]]],[[.,[[.,.],.]],.]]
[1,1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0,0,0,0,1,0]=>[[[.,.],[[.,[.,.]],.]],[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0,0,0,1,0]=>[[[.,.],[[.,.],[.,.]]],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[[.,[.,[[.,[[[.,[[.,.],.]],.],.]],[.,.]]]],[.,.]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0,1,0,0]=>[[[.,.],[[[.,.],.],[[.,.],.]]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0,0]=>[[.,[.,[[[[[[.,.],.],[.,.]],.],[.,.]],.]]],[.,.]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0,0]=>[[[[[[.,.],.],[.,.]],[[.,.],.]],[[.,.],.]],[.,.]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,[[[.,.],.],.]],[[.,.],.]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,1,0,0]=>[[.,[.,[[[[.,.],[[.,.],.]],[.,.]],.]]],[[.,.],.]]
[1,1,1,1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[[[[.,.],[[.,.],.]],[[[.,[[.,.],.]],.],.]],[.,.]]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,.]]],[[.,[[[.,[[.,.],.]],.],.]],.]]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,1,0]=>[[[.,.],[[.,[.,.]],.]],[[[[.,.],.],[.,[.,.]]],.]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[[.,[.,[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]]],[.,.]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,[.,.]],[.,[.,.]]]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]]],[.,.]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[[[[[.,[.,.]],[.,.]],[.,[.,.]]],[[.,.],.]],[.,.]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,1,1,1,0,0,0,1,0,0,0]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[[.,[.,[[.,[.,.]],.]]],[[[.,[.,[[.,.],.]]],.],.]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[[.,[.,.]],[[[.,.],.],[[[.,[.,[[.,.],.]]],.],.]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[[.,.],.],.]],.],[[[.,[.,[[.,.],.]]],.],.]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[.,.],.],[.,[.,[[.,.],[.,[.,.]]]]]],.],[.,.]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[.,.]],[[[[.,.],.],.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[[[.,[[[[.,.],.],.],.]],.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[[[[[[.,[[.,[.,.]],[.,.]]],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[[[[[.,[.,[[.,[.,.]],.]]],.],[.,.]],.],[[.,.],.]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[[.,[.,[[.,[.,.]],.]]],[[[[.,.],[[.,.],.]],.],.]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[[.,.],[.,[.,[[[.,[.,.]],.],.]]]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],.],[[[[.,.],[[.,.],.]],.],.]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[[[.,[[[.,.],.],.]],.],[[[[.,.],[[.,.],.]],.],.]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[.,.],.],[.,[.,[[[.,[.,.]],.],.]]]],.],[.,.]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[[[.,.],.],.],[[[.,.],.],[[.,.],.]]]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[[[.,[[[[.,.],.],.],.]],.],[[[.,.],.],[[.,.],.]]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[[[[.,[[[.,.],.],.]],.],.],[[.,.],.]],.],[.,.]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[[[[[.,[.,.]],.],[[[.,[.,.]],.],.]],.],[[.,.],.]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[[.,[.,.]],[[[[[.,[[.,.],.]],.],.],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[[[.,[[[[[.,[[.,.],.]],.],.],.],.]],.],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[[[[[[[[.,.],.],[.,[.,.]]],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[[[[[[[.,[.,.]],.],[.,.]],.],[.,.]],.],[[.,.],.]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0,0,1,1,0,0,0]=>[[[[[.,.],[[.,.],[.,.]]],[.,.]],.],[[[.,.],.],.]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[[.,[.,[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]]],[.,.]]
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0,0,0,1,0,0]=>[[[[.,.],[[.,.],.]],[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,0,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0]=>[[.,[.,[[[.,.],[[.,.],.]],.]]],[.,[[.,[.,.]],.]]]
[1,1,1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,1,0]=>[[[[.,.],[[.,.],[.,.]]],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0,0,0,0,1,0]=>[[[.,.],[.,[[.,.],.]]],[[.,[[.,.],[.,[.,.]]]],.]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[[.,[.,[[.,[.,[[[[.,.],.],[.,.]],.]]],.]]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[[.,[[[.,.],.],.]],[[.,.],.]],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0]=>[[.,[.,.]],[[[[[.,.],.],[.,.]],[[.,.],.]],[.,.]]]
[1,1,1,1,0,0,1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0,0,0]=>[[[.,[[[.,.],.],[.,.]]],.],[[.,[[[.,.],.],.]],.]]
[1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0,0,1,0,0]=>[[[[[[.,.],.],.],[[.,.],.]],.],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],[[.,.],.]],[[.,[[.,.],.]],.]]]
[1,1,1,1,0,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[[[.,[[.,.],[[.,.],.]]],.],[[[.,.],[[.,.],.]],.]]
[1,1,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[[[[.,.],[[.,.],.]],.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0,0,0,1,0]=>[[[[.,.],[[.,.],[.,.]]],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[[.,[.,[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0,1,0]=>[[[[[.,.],[.,[.,.]]],[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0,0]=>[[[.,[[.,.],[[.,.],[.,.]]]],.],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,1,0,0,0]=>[[[[.,.],[.,[[.,.],.]]],.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,[.,[[.,[.,.]],.]]]],[[.,.],.]]]
[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0,0,1,0]=>[[[.,[[.,[[.,.],.]],[.,[.,.]]]],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[.,[.,[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[[[.,[.,[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]]],.],.]
[1,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0,0,1,0]=>[[[[.,[[.,[[.,.],.]],[.,[.,.]]]],[.,[.,.]]],.],.]
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[[.,.],[.,[.,[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]]]]
[1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[[[.,[.,[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]]],.],.]
[1,1,0,1,0,1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0,0]=>[[[[.,[[.,[.,.]],[.,.]]],[[.,[[.,.],.]],.]],.],.]
[1,1,0,1,0,1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[[[[[[.,[.,.]],.],[.,.]],[.,[[.,[.,.]],.]]],.],.]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,[.,.]]],[[[.,.],.],[[.,.],.]]]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0,1,0]=>[[[.,[[.,[.,.]],[[[.,[.,.]],.],.]]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[[.,.],[.,[.,[[.,[.,.]],[[[.,.],.],[[.,.],.]]]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[.,[.,[[.,[.,.]],[[[.,.],.],[[.,.],.]]]]],.],.]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0,0,1,0]=>[[[[.,[[.,[.,.]],[[[.,[.,.]],.],.]]],[.,.]],.],.]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[.,[.,[[[.,[[[.,.],.],.]],.],[[.,.],.]]]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,[.,[[[.,[[[.,.],.],.]],.],[[.,.],.]]]],.],.]
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[[[[.,[[[[[.,.],.],.],[[.,.],.]],.]],[.,.]],.],.]
[1,1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[[[[[[.,.],[[[.,[.,.]],.],.]],[.,.]],[.,.]],.],.]
[1,1,1,0,0,0,1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[[.,.],[.,[.,[[[[[.,.],.],[.,[.,.]]],.],[.,.]]]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[[[.,[.,[[[[[.,.],.],[.,[.,.]]],.],[.,.]]]],.],.]
[1,1,0,1,0,1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[[[[.,[[[[.,.],.],[.,[.,.]]],.]],[[.,.],.]],.],.]
[1,1,0,1,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[[[[[[[.,[.,.]],.],[.,.]],[[.,.],.]],[.,.]],.],.]
[1,1,0,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,1,0,0,0]=>[[[[[.,.],[[.,.],[.,.]]],[[.,[[.,.],.]],.]],.],.]
[1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]],[.,[.,.]]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0,0]=>[[[[.,[[.,[.,.]],[.,.]]],[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,[.,.]]],[.,.]]]
[1,1,1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[[[.,[[.,.],[.,[.,.]]]],.],[[.,[[.,.],[.,.]]],.]]
[1,1,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0,0,0]=>[[[[.,.],[.,.]],.],[.,[[.,[.,[[.,[.,.]],.]]],.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[.,.]],[[.,[.,[.,.]]],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[[[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[[.,.],[.,[.,[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[.,[.,[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]]],.],.]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[[[[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]],[.,.]],.],.]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[[.,.],[.,[.,[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[[[.,[.,[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]]],.],.]
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[[[[.,[[[.,.],[.,.]],.]],[.,[[.,[.,.]],.]]],.],.]
[1,1,0,1,0,1,1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[[[[[[[.,.],[.,.]],[.,.]],[.,[.,.]]],[.,.]],.],.]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[[.,[.,.]],[[.,[.,.]],[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[[[.,[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]],.],[.,.]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[[.,.],[.,[.,[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]]],.],.]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[[[[.,[[.,[.,[.,[.,.]]]],.]],[[.,.],[.,.]]],.],.]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[.,.],[.,[.,[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]]],.],.]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,.],[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]],.],.]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[[[[.,.],.],[[.,[.,[.,.]]],[[.,.],[.,.]]]],.],.]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[.,.],[.,[.,[[[[.,[[.,[.,.]],.]],[.,.]],.],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[[.,[.,[[[[.,[[.,[.,.]],.]],[.,.]],.],.]]],.],.]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[[[.,.],[[[[.,[[.,[.,.]],.]],[.,.]],.],.]],.],.]
[1,1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[[[[.,.],.],[[[[.,.],[.,.]],[.,.]],[.,.]]],.],.]
[1,1,0,1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[[[[[[.,[[.,[[.,.],.]],[.,.]]],.],.],[.,.]],.],.]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[[.,[.,.]],[[.,[.,.]],[.,[.,[[[.,[.,.]],.],.]]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[.,[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]],.],[.,.]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[[.,.],[.,[.,[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[.,[.,[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]]],.],.]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[[.,[[.,[.,[.,.]]],.]],[.,[.,[[.,.],.]]]],.],.]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[.,.],[.,[.,[[[.,[.,[[[.,[.,.]],.],.]]],.],.]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[[.,.],[[[.,[.,[[[.,[.,.]],.],.]]],.],.]],.],.]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[[[.,.],.],[[.,[.,.]],[.,[.,[[.,.],.]]]]],.],.]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[.,.],[.,[.,[[[[.,.],[[[.,[.,.]],.],.]],.],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,[.,[[[[.,.],[[[.,[.,.]],.],.]],.],.]]],.],.]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[[[.,.],[[[[.,.],[[[.,[.,.]],.],.]],.],.]],.],.]
[1,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[[[.,.],.],[[[.,.],.],[[[.,[.,.]],.],.]]],.],.]
[1,1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[[[[.,[[.,.],.]],.],.],[.,[.,[[.,.],.]]]],.],.]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[.,.],[.,[.,[[[[[.,.],.],[[.,.],[.,.]]],.],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[[.,[.,[[[[[.,.],.],[[.,.],[.,.]]],.],.]]],.],.]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[[[.,.],[[[[[.,.],.],[[.,.],[.,.]]],.],.]],.],.]
[1,1,0,1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[[[[.,.],.],[[[[.,.],.],.],[[.,.],[.,.]]]],.],.]
[1,1,0,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[[[[.,[[[.,[[.,.],.]],.],.]],.],.],[.,.]],.],.]
[1,1,0,1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[[[[.,[.,.]],.],[[.,.],.]],.],.],[.,.]],.],.]
[1,0,1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[[[[.,[.,.]],.],[[.,.],.]],[.,.]]],.],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[.,[.,.]],[.,[[[[.,.],.],.],[[.,[.,.]],.]]]],.]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]],.]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,[[[.,.],.],.]],[[[[.,.],[.,.]],.],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[.,[[[.,.],.],.]],[[[[.,.],.],[.,.]],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[.,[[.,.],[[.,[[[.,.],.],.]],.]]]],.]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[.,[[[.,.],.],.]],[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[.,[[[.,.],.],.]],[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[[.,.],[[.,[.,[[[.,.],.],.]]],.]],.],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[.,[[[.,.],.],.]],[[.,.],[.,[[[.,[.,.]],.],.]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[[.,.],[[.,[[[.,[.,.]],.],.]],.]],.],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[[.,.],[[.,[[[.,.],.],.]],[.,.]]],.],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[[.,.],[[[[.,[.,.]],.],.],[.,.]]],.],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[.,[[.,[.,.]],[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[[[[[.,[[[.,.],.],[.,.]]],.],.],[[[.,.],.],.]],.]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[[[[[.,[[[.,.],[.,.]],[.,[.,.]]]],.],.],[.,.]],.]
[1,0,1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[[.,[.,.]],[[[[.,.],[.,.]],.],[.,[.,.]]]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[.,[.,[[.,[.,.]],[[[[.,.],.],[.,.]],[.,[.,.]]]]]]
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[.,[[[[.,[[[.,.],.],[[.,[.,.]],.]]],.],.],[.,.]]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[[[[[.,[.,.]],[.,.]],[[[.,.],.],.]],[.,[.,.]]],.]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,[.,.]]]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[[[[[.,[.,.]],[.,.]],[.,[.,.]]],[[[.,.],.],.]],.]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[[[[[.,[[[.,.],.],.]],[.,.]],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[[[.,[[[.,.],.],.]],.],[.,.]],[[[.,.],.],.]],.]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[[.,.],.],.],[[.,[[[.,.],.],.]],[.,.]]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[.,[.,[[[[.,.],.],.],[[[[.,[.,.]],.],.],[.,.]]]]]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[[[[[.,[[[.,.],.],[.,[.,[.,.]]]]],.],.],[.,.]],.]
[1,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[[.,[[[.,.],[[.,.],.]],[[[.,.],.],.]]],[.,[.,.]]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[[[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0,1,0]=>[[[[[.,[.,.]],.],[.,[.,[.,.]]]],[[[.,.],.],.]],.]
[1,1,1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[[.,[[[.,.],[[.,.],.]],[.,[.,.]]]],[[[.,.],.],.]]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[[.,[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0,1,0]=>[[.,[[[.,.],.],[[.,[.,[.,.]]],.]]],[[[.,.],.],.]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0,1,0]=>[[[[.,[.,.]],[[.,[.,[.,.]]],.]],.],[[[.,.],.],.]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[[.,[[[.,.],.],.]],[[.,.],.]],.],[[[.,.],.],.]]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[[.,[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[[.,[[[.,.],.],[[.,[.,.]],[.,.]]]],[[[.,.],.],.]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[[[[.,[.,.]],[[.,[.,.]],[.,.]]],.],[[[.,.],.],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[.,[[[[[.,.],.],.],[.,[[[.,[.,.]],[.,.]],.]]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[.,[[[[[.,.],.],.],[.,[[.,[.,.]],[[.,.],.]]]],.]]
[1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,[.,[[[[.,[.,.]],.],[[.,.],.]],[.,.]]]],.],.]
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[.,[.,.]],[[.,[[[[.,.],.],.],[[.,[.,.]],.]]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[.,.]],[[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[[.,[.,.]],.],.],[[[[.,.],[.,.]],.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[[.,[.,.]],.],.],[[[[.,.],.],[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[.,[[.,.],[[.,[[[.,.],.],.]],.]]],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[[.,[.,.]],.],.],[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[[.,[.,.]],.],.],[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[[.,.],.],[[.,[.,[[[.,.],.],.]]],.]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[[.,.],.],[[.,[.,.]],[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[[.,[.,.]],.],.],[[.,.],[.,[[[.,[.,.]],.],.]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[[.,.],.],[[.,[[[.,[.,.]],.],.]],.]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[[.,.],.],[[.,[[[.,.],.],.]],[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[[.,.],.],[[[[.,[.,.]],.],.],[.,.]]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[[[.,[[[[[.,[.,.]],.],[.,[.,.]]],[.,.]],.]],.],.]
[1,1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[[.,[.,.]],[[.,[[[.,.],.],[.,.]]],[[[.,.],.],.]]]
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[[.,[.,.]],[[.,[[[.,.],[.,.]],[.,[.,.]]]],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[[.,[[[[[.,.],[.,.]],.],[.,[.,.]]],.]],.],.]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[.,[[[.,[[[[[.,.],.],[.,.]],[.,[.,.]]],.]],.],.]]
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[[.,[[.,[[[.,.],.],[[.,[.,.]],.]]],[.,.]]],.],.]
[1,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[[.,[.,.]],[[[[.,[.,.]],[.,.]],.],[[[.,.],.],.]]]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[.,[[[[.,[.,.]],[[.,[.,.]],.]],.],[.,.]]],.],.]
[1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,[[[[.,[.,.]],.],[[.,[.,.]],.]],[.,.]]],.],.]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[[[[.,[[[.,.],.],.]],[.,.]],.],[.,.]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[[[[.,[[[.,.],.],.]],.],[.,.]],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[[.,[[.,.],[[.,[[[.,.],.],.]],[.,.]]]],.],.]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[[.,[[.,.],[[[[.,[.,.]],.],.],[.,.]]]],.],.]]
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[[.,[.,.]],[[.,[[[.,.],.],[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[[[[.,[[[.,.],[[.,.],.]],.]],.],.],[[[.,.],.],.]]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[[.,[.,.]],[[[[.,[.,.]],[.,[.,[.,.]]]],.],[.,.]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,0]=>[[.,[.,.]],[[[[.,[.,.]],.],[.,[.,[.,.]]]],[.,.]]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[[.,[[[.,.],[[.,.],.]],[.,[.,.]]]],.],.],[.,.]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[[[[.,[[[.,.],[[.,[.,[.,.]]],.]],.]],.],.],[.,.]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,1,0]=>[[[[.,[[[.,.],.],[[.,[.,[.,.]]],.]]],.],.],[.,.]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0,1,0]=>[[[[.,[.,.]],[[.,[.,[.,.]]],.]],[.,.]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[[.,[[[.,.],.],.]],[[.,.],.]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[[[[.,[[[.,.],[[.,[.,.]],[.,.]]],.]],.],.],[.,.]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[[[[.,[[[.,.],.],[[.,[.,.]],[.,.]]]],.],.],[.,.]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[[[[.,[.,.]],[[.,[.,.]],[.,.]]],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[.,[[.,[.,.]],[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]]]
[1,1,0,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[[[.,[[[.,.],[[.,[.,.]],.]],.]],[[.,.],[.,.]]],.]
[1,0,1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[.,[.,[[[.,[[[.,.],.],[.,.]]],[[[.,.],.],.]],.]]]
[1,0,1,0,1,1,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[[[.,[[[.,.],[.,.]],[.,[.,.]]]],[.,.]],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[.,[.,[[[[[.,.],[.,.]],.],[.,[.,.]]],.]]],.],.]
[1,1,0,1,0,0,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[.,[.,[[[[[.,.],.],[.,.]],[.,[.,.]]],.]]],.],.]
[1,1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0]=>[[[.,[[.,.],[[.,.],.]]],[.,[[[.,.],.],[.,.]]]],.]
[1,0,1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[.,[.,[[[[[.,[.,.]],[.,.]],.],[[[.,.],.],.]],.]]]
[1,1,0,1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,0,0]=>[[[.,[[.,.],[.,[.,.]]]],[[[[.,.],.],[.,.]],.]],.]
[1,1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0]=>[[[.,[[.,.],[[.,[.,.]],.]]],[[[.,.],.],[.,.]]],.]
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[.,[.,[[[[[.,[.,.]],[.,.]],[.,[.,.]]],[.,.]],.]]]
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[[[.,[[[.,.],.],.]],[.,.]],.],[.,.]],.]]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[[[.,[[[.,.],.],.]],.],[.,.]],[.,.]],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,[.,[[.,.],[[.,[[[.,.],.],.]],[.,.]]]]],.],.]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[.,[.,[[.,.],[[[[.,[.,.]],.],.],[.,.]]]]],.],.]
[1,1,0,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0,0]=>[[[[[.,.],[[.,.],.]],.],[.,[[.,[.,.]],[.,.]]]],.]
[1,0,1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[.,[.,[[.,[[[.,.],[[.,.],.]],.]],[[[.,.],.],.]]]]
[1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0]=>[[[[[.,.],[.,[.,.]]],.],[[[.,[.,.]],[.,.]],.]],.]
[1,1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,0]=>[[[[[.,.],[[.,[.,.]],.]],.],[[.,[.,.]],[.,.]]],.]
[1,0,1,0,1,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[.,[.,[[.,[[[.,.],[[.,.],.]],[.,[.,.]]]],[.,.]]]]
[1,1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,0,0]=>[[[[.,.],[.,.]],[.,[[[[.,[.,.]],.],[.,.]],.]]],.]
[1,1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,0]=>[[[[.,.],[[.,.],.]],[.,[[[.,[.,.]],.],[.,.]]]],.]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0,0]=>[[[[.,.],[.,[.,.]]],[[[[.,[.,.]],.],[.,.]],.]],.]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[.,[.,[[[[.,[[[.,.],.],.]],[[.,.],.]],.],[.,.]]]]
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[.,[.,[[.,[[[.,.],[[.,[.,.]],[.,.]]],.]],[.,.]]]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[.,[.,[[.,[[[.,.],.],[[.,[.,.]],[.,.]]]],[.,.]]]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[.,[.,[[[[.,[.,.]],[[.,[.,.]],[.,.]]],.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,[[[.,.],[.,[[[.,[.,.]],[.,.]],.]]],.]],.],.]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,[[[.,.],[.,[[.,[.,.]],[[.,.],.]]]],.]],.],.]
[1,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[[.,[[[.,.],[[.,.],.]],.]],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[[.,[[[.,.],[.,[.,.]]],.]],[[[.,.],[[.,.],.]],.]]
[1,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0,0]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>[.,[[[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]],[.,.]],.]]
[1,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,0,1,0,0]=>[[.,[[.,.],[.,.]]],[.,[[[[.,.],.],[[.,.],.]],.]]]
[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0]=>[[.,[[.,.],[.,[.,.]]]],[[[[.,.],.],[[.,.],.]],.]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0,1,0]=>[.,[[[[[.,[[[.,.],.],.]],[.,[.,.]]],.],[.,.]],.]]
[1,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[[[[.,.],[.,.]],.],[.,[[[.,[.,.]],[[.,.],.]],.]]]
[1,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0,1,0,0]=>[[[[.,.],[[.,.],.]],.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,1,0,0]=>[[[[.,.],[.,[.,.]]],.],[[[.,[.,.]],[[.,.],.]],.]]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,.],[.,.]],[.,[[[[.,[.,.]],.],[[.,.],.]],.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0,1,0]=>[.,[[.,[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[.,[[[.,[[[.,.],[.,[[[.,.],.],.]]],.]],[.,.]],.]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[.,[[[.,[[[.,.],.],[.,[[[.,.],.],.]]]],[.,.]],.]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[.,[[[[[.,[.,.]],[.,[[[.,.],.],.]]],.],[.,.]],.]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>[.,[[.,[[[.,.],[[.,[[[.,.],.],.]],.]],.]],[.,.]]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[[[.,.],[.,[.,[[[.,.],.],.]]]],.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[[.,.],[.,[[[.,[.,.]],.],.]]],.]],[.,.]],.]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],.],[[.,[[.,[.,.]],.]],.]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[[.,[.,.]],.],.],[[.,[[[.,.],[.,[.,.]]],.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,.],[[[.,.],[[.,.],.]],.]]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],.],.],[[.,[.,.]],[.,[[.,[.,.]],.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[.,[[[.,.],[.,[[[.,.],.],.]]],.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[.,.]],[[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[[[.,[[[.,[.,[.,.]]],.],[[.,.],[[.,.],.]]]],.],.]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[[.,[[.,.],[[[.,.],[[.,[.,.]],[.,.]]],.]]],.],.]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[.,.]],[[.,[[[.,[[.,.],.]],[.,[.,.]]],.]],.]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[[.,[[.,.],[[.,[.,[[.,.],.]]],[[.,.],.]]]],.],.]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[[.,[[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]],.]],.],.]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,[[.,[[[.,[[[.,.],.],.]],[.,.]],.]],.]],.],.]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[[[[.,[[[.,.],.],.]],.],.],[[.,[[.,[.,.]],.]],.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[.,[.,.]],[[.,[.,.]],[.,[[[.,.],[.,[.,.]]],.]]]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[[[.,[[[[.,.],.],[[[.,.],[[.,.],.]],.]],.]],.],.]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[.,[.,.]],[[[[.,[.,.]],.],.],[.,[[.,[.,.]],.]]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,[[.,[.,.]],[[.,.],[.,[[[.,.],.],.]]]]],.],.]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[[[.,[[[[.,[.,.]],.],.],[[.,.],[.,[.,.]]]]],.],.]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[[.,[.,.]],.],.],[[.,.],[[.,.],.]]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[[.,[.,[.,.]]],.],[[.,.],[[.,[.,.]],[.,.]]]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,[[.,[.,.]],[[.,[[.,.],.]],[.,[.,.]]]]],.],.]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[.,[[[.,[.,[[.,[.,[[.,.],.]]],.]]],.],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,.],[[[[.,[.,[[.,[.,.]],.]]],.],[.,.]],.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[.,.],[[[.,.],[[.,[[[.,.],.],.]],[.,.]]],.]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[[.,[.,.]],[[.,[[[.,.],.],.]],[.,[[.,[.,.]],.]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[[[.,[[[.,[[.,.],.]],[.,[[[.,.],.],.]]],.]],.],.]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[[[.,[[.,[[[.,.],.],.]],[[.,.],[.,[.,.]]]]],.],.]
[1,0,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[[[.,.],.],.],.]],.],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,.],[[.,[.,[[.,.],.]]],[[.,[.,.]],[.,.]]]]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[[[.,[[[[[.,[[.,.],.]],.],.],[.,[.,.]]],.]],.],.]
[1,0,1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[.,[[.,.],[[[[[.,[[.,.],.]],.],.],.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[.,[[.,[[[[[.,[[.,[.,.]],.]],.],.],.],[.,.]]],.]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[.,[[.,[[.,[.,[[.,[[[.,.],.],.]],.]]],[.,.]]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[[[.,[[[.,[[[.,.],[.,[.,.]]],.]],[.,.]],.]],.],.]
[1,0,1,1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[.,[[.,.],[[.,[[[[.,.],[[.,.],.]],.],.]],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[.,[[.,[[[[.,[.,.]],[.,.]],.],.]],[.,.]]],.]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[.,[[.,[[[[[[[.,.],.],[.,.]],.],.],[.,.]],.]],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[.,[[[.,[[[.,.],[.,.]],.]],[.,[.,.]]],.]],.]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[.,[[[.,.],.],.]],[[.,[[[.,.],[.,[.,.]]],.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],[.,[[.,.],[[[.,.],[[.,.],.]],.]]]],.]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,[.,.]],[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]],.]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[.,[[[.,.],.],.]],[[.,[.,.]],[.,[[.,[.,.]],.]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[.,[[[.,.],[.,[[[.,.],.],.]]],.]]],.]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]],.]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[.,[.,.]]],[[.,.],[[.,.],.]]],[.,.]],.]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[[[.,.],.],[[[.,.],[[.,[.,.]],[.,.]]],.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]],.]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[.,[[[[.,.],.],[[.,[.,[[.,.],.]]],[[.,.],.]]],.]]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[.,[[[.,.],[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]],.]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[[.,.],[.,[[[.,[[[.,.],.],.]],[.,.]],.]]],.]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[[.,[[[.,.],.],[[.,[[.,[.,.]],.]],.]]],[.,[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[[[.,[.,.]],.],.],[.,[[[.,.],[.,[.,.]]],.]]],.]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[.,[[.,[.,.]],[[[.,.],.],[[[.,.],[[.,.],.]],.]]]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[[[.,[.,.]],.],[.,[[.,[.,.]],.]]],[.,[.,.]]],.]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[.,[[[[.,[.,.]],.],.],[[.,.],[.,[[[.,.],.],.]]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[.,[[[[.,[.,.]],.],[[.,.],[.,[.,.]]]],[.,[.,.]]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[.,[.,.]],.],[[.,.],[[.,.],.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[[[[[.,[.,.]],.],.],.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[.,[[[[.,[.,.]],.],.],[[.,[[.,.],.]],[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[[[[[.,[[.,[.,[[.,.],.]]],.]],.],.],.],[[.,.],.]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[[.,[.,[.,.]]],[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,[.,.]]],[[.,.],[[.,[[[.,.],.],.]],[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[[[[[.,[[[.,.],.],.]],.],.],[.,[[.,[.,.]],.]]],.]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[.,[[.,[.,.]],[[.,[[.,.],.]],[.,[[[.,.],.],.]]]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[.,[[[[.,[[[.,.],.],.]],.],.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[[[[[[[.,.],.],.],[[.,.],[[.,.],.]]],.],.],[.,.]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[[.,[.,[[.,[.,[[.,.],.]]],.]]],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[.,[[.,[.,.]],[[[[.,[[.,.],.]],.],.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[[.,[.,[[[[.,[[.,.],.]],.],.],[[.,.],.]]]],[.,.]]
[1,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[[[[[[[.,[[.,[.,.]],.]],.],.],[.,.]],[.,.]],.],.]
[1,1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[[[[[.,[.,[[.,[[[.,.],.],.]],.]]],.],[.,.]],.],.]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[.,[[.,[.,.]],[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[[.,[.,[[.,[[[[.,.],[[.,.],.]],.],.]],.]]],[.,.]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[[[[[.,[[[[.,[.,.]],[.,.]],.],.]],.],[.,.]],.],.]
[1,1,0,1,0,1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[[[[.,.],[[[[[[.,.],.],[.,.]],.],.],[.,.]]],.],.]
[1,1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[[.,.],[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]],.],.]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,0,1,0]=>[[.,[[[.,.],[[.,[[.,[.,.]],.]],.]],.]],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,[[[.,.],.],.]],[.,[[[.,.],[.,[.,.]]],.]]],.]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0,0]=>[.,[[[.,[[.,.],[[[.,.],[[.,.],.]],.]]],[.,.]],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[.,[[[.,[[.,.],.]],[.,[[[.,[.,.]],[.,.]],.]]],.]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[[[.,[.,.]],[.,[[.,[.,.]],.]]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[.,[[.,[[[.,.],.],.]],[[.,.],[.,[[[.,.],.],.]]]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,0,0,1,0]=>[.,[[[[.,[.,.]],[[.,.],[.,[.,.]]]],.],[.,[.,.]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[.,[.,.]],[[.,.],[[.,.],.]]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[[.,[[[[.,.],.],.],.]],[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[.,[[.,[[[.,.],.],.]],[[.,[[.,.],.]],[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0]=>[[.,[[[[.,[.,[[.,.],.]]],[[.,.],.]],.],.]],[.,.]]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[[[.,[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]],[.,.]],.]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,[.,[[.,.],.]]],[[.,[[[.,.],.],.]],[.,.]]],.]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[[[.,.],.],[.,[[.,[.,.]],.]]]],[.,[.,.]]],.]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[.,[[[[[.,[[.,.],.]],.],.],[.,[[[.,.],.],.]]],.]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0,1,0]=>[.,[[.,[[[.,.],.],[[.,.],[.,[.,.]]]]],[.,[.,.]]]]
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,1,0,0,1,0,0]=>[[.,[[[.,.],.],[[.,.],[[.,.],.]]]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[[[[[[.,[[.,.],.]],.],.],.],[[.,[.,.]],[.,.]]],.]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0,0,1,0]=>[.,[[[[[.,[[.,.],.]],.],[.,[.,.]]],[.,[.,.]]],.]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0,1,0,0]=>[[[[[.,[[.,.],.]],.],[[.,.],.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0,0]=>[.,[[[[.,[[.,[.,.]],.]],.],[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[.,[[[[[.,[[.,[[[.,.],.],.]],.]],.],.],.],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[.,[[[[[.,[[[.,.],[.,[.,.]]],.]],.],.],[.,.]],.]]
[1,1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0]=>[[[[[[[[.,.],[[.,.],.]],.],[.,.]],.],.],[.,.]],.]
[1,0,1,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[[[[[[.,[.,.]],[.,.]],.],[.,.]],.],.],[.,.]]]
[1,0,1,1,1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0,0]=>[.,[[.,[.,[[[[[.,.],.],[.,.]],.],[.,.]]]],[.,.]]]
[1,0,1,1,1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[.,[.,[[.,[[[.,.],[.,.]],.]],.]]],[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0]=>[[[.,[[[.,.],[.,[[.,[.,.]],.]]],.]],[.,[.,.]]],.]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,0,1,0]=>[.,[[.,[[[.,.],[[.,.],[.,[.,.]]]],.]],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0,1,0,0]=>[[.,[[[.,.],[[.,.],[[.,.],.]]],.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[[[.,[[[[.,.],[[.,[.,.]],[.,.]]],.],.]],[.,.]],.]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0,0,1,0]=>[.,[[[[[.,[[.,.],.]],[.,[.,.]]],.],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0,1,0,0]=>[[[[[.,[[.,.],.]],[[.,.],.]],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,0,0]=>[.,[[[[.,[[.,[.,.]],.]],[.,.]],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[.,[[.,[[[[.,[[[.,.],.],.]],[.,.]],.],.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0]=>[.,[[[.,[[[.,.],[.,[.,.]]],[.,.]]],[.,[.,.]]],.]]
[1,1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,1,0,0]=>[[[.,[[[.,.],[[.,.],.]],[.,.]]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,0,0]=>[.,[[.,[[[.,[.,.]],[.,.]],[.,.]]],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0,0,0]=>[.,[[[[[[.,.],.],[.,.]],[.,.]],[.,[.,[.,.]]]],.]]
[1,0,1,1,0,1,1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[.,[[[[[[[.,.],[.,.]],[.,[.,.]]],.],.],[.,.]],.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,1,0,0]=>[[[.,[[[.,.],[[.,.],.]],.]],[.,[.,[[.,.],.]]]],.]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,0,0]=>[.,[[.,[[[.,[.,.]],[.,.]],.]],[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0,0]=>[.,[[[[[[.,.],.],[.,.]],.],[.,[.,[[.,.],.]]]],.]]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0]=>[.,[[[.,[[.,.],[.,.]]],[.,[.,[[.,[.,.]],.]]]],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[[.,[.,.]],.],.],[[.,[.,[[.,.],[[.,.],.]]]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[.,[.,.]],[[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[.,[.,.]],[[.,[[[.,[[.,.],[.,[.,.]]]],.],.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,[[.,[[.,.],[[.,.],.]]],.]]],.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,[[[[.,.],.],[[.,.],.]],.]]],.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]],.]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[.,[[[.,.],.],[[.,[[.,[.,.]],.]],.]]]],.],.]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]]],.],.]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,[[[.,[[.,[[.,.],[.,[.,.]]]],.]],.],.]],.],.]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]],.],.]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[[.,[[[.,[[[[.,.],.],[[.,.],.]],.]],.],.]],.],.]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[[.,[[[.,[[.,[[.,[.,.]],.]],[.,.]]],.],.]],.],.]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,[[[.,.],.],.]],[.,[[.,[.,.]],.]]]],.],.]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]],.]],.],.]
[1,1,0,1,0,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[[.,[.,[.,[[[.,.],.],[[.,.],[[.,.],.]]]]]],.],.]
[1,1,0,1,0,0,1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[[[.,[.,[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]]],.],.]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[.,[.,[.,[[.,.],[[[.,.],.],[[.,.],.]]]]]],.],.]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[[.,[.,[[[.,[[[.,[.,.]],.],[.,.]]],.],.]]],.],.]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[.,[.,[[[.,[[.,.],[[.,.],.]]],[.,.]],.]]],.],.]
[1,1,0,1,0,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[.,[.,[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]]],.],.]
[1,1,0,1,0,0,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[.,[.,[[[[[[.,.],.],[.,.]],.],[.,.]],.]]],.],.]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[.,[.,[[[.,.],.],[[.,[[.,[[.,[.,.]],.]],.]],.]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[.,[[[.,.],.],.]],[[.,[.,[[.,.],[[.,.],.]]]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,.]],[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]],.]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[[.,[.,.]],[.,[.,[[[[.,.],.],[[.,.],.]],.]]]],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[[.,[.,.]],[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]],.]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[.,[.,[[[.,[.,.]],.],[.,[[.,[[.,[.,.]],.]],.]]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[[[.,[.,.]],.],.],[.,[.,[[.,.],[[.,.],.]]]]],.]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[.,[.,[[.,[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]],.]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[.,[[[.,[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]],.],.]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[.,[.,[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[.,[.,.]],[[.,[[[[.,.],.],[[.,.],.]],.]],.]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[.,[[[[.,[[[.,.],.],.]],.],.],[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[.,[[.,[.,.]],[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[.,[[[.,.],.],[[.,.],[[.,.],.]]]]],.],.]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[.,[[[.,[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]],.],.]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[.,[[[.,[.,[[.,.],[[[.,.],.],[[.,.],.]]]]],.],.]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[.,[[[.,[[[.,[[[.,[.,.]],.],[.,.]]],.],.]],.],.]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[[.,[[[.,[[.,.],[[.,.],.]]],[.,.]],.]],.],.]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[[.,[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]],.],.]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[.,[[[.,[[[[[[.,.],.],[.,.]],.],[.,.]],.]],.],.]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0,1,0]=>[.,[.,[[[[.,.],[[.,[[.,[.,.]],.]],.]],[.,.]],.]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,[[[.,.],.],.]],[.,[.,[[.,.],[[.,.],.]]]]],.]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0]=>[.,[.,[[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]],[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[.,[[[.,[.,.]],[.,[[.,[[.,.],[.,[.,.]]]],.]]],.]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[.,[.,[.,[[[.,.],.],[[.,[[.,.],[[.,.],.]]],.]]]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[[.,[.,.]],[.,[[[[.,.],.],[[.,.],.]],.]]],.]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[[.,[.,.]],[.,[[.,[[.,[.,.]],.]],[.,.]]]],.]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[.,[.,[[[[.,[[.,.],.]],.],[.,[[.,[.,.]],.]]],.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[.,[.,[[.,[[.,[.,.]],.]],[.,[[.,.],[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[.,[.,[.,[[[.,[.,.]],.],[.,[[.,.],[[.,.],.]]]]]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[.,[.,[[[.,.],[[.,[[[.,.],.],[.,[.,.]]]],.]],.]]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[.,[.,[.,[[.,[[[.,[[.,.],.]],.],[[.,.],.]]],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[.,[.,[[[.,[[.,[[[.,[.,.]],.],[.,.]]],.]],.],.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[.,[.,[[.,[.,.]],[[.,[[.,.],[[.,.],.]]],[.,.]]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[[.,[[[.,[.,.]],[.,.]],.]],.],.],[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[.,[.,[[.,[.,.]],[[[[[.,.],.],[.,.]],.],[.,.]]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0]=>[.,[[.,[[[.,.],[.,[[.,[.,.]],.]]],.]],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[.,[[[.,[[[.,.],.],.]],[.,[[.,.],[.,[.,.]]]]],.]]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[.,[.,[.,[[[[.,.],[[.,.],[[.,.],.]]],[.,.]],.]]]]
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[.,[.,[[.,[[[.,[[.,.],.]],[.,[.,.]]],.]],[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[.,[.,[.,[[[[.,.],.],[[[.,.],.],[[.,.],.]]],.]]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[.,[.,[[[.,[.,.]],[.,[[[.,[.,.]],.],[.,.]]]],.]]]
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[.,[.,[[[[[[.,.],[.,[.,.]]],[.,.]],.],[.,.]],.]]]
[1,0,1,0,1,0,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[.,[.,[.,[[.,[[[.,.],[[.,.],.]],[.,.]]],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[.,[.,[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[[[[[.,.],.],[.,.]],[.,.]],.],[.,.]]]]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[.,[.,[[[.,[[[.,.],[[.,.],.]],.]],[[.,.],.]],.]]]
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[[[.,[.,.]],[.,.]],.]],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[.,[.,[[[[[[.,.],.],[.,.]],.],[.,[[.,.],.]]],.]]]
[1,0,1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[.,[.,[[[.,[[.,.],[.,.]]],[.,[[.,[.,.]],.]]],.]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],[[[.,[.,.]],.],.]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[[.,[[[.,.],.],.]],.],[.,.]],[[[.,[.,.]],.],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[.,[[[.,[.,.]],.],.]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[[.,[.,.]],.],[.,[.,[[[.,.],.],.]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],[[[.,[.,.]],.],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[[.,[[[.,.],.],.]],.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[[.,[[[.,.],.],[.,.]]],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[[[.,[.,.]],.],.],[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[[[.,[.,.]],.],.],[.,[[[.,[[[.,.],.],.]],.],.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[[.,[[[.,.],[.,.]],.]],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[[[.,[.,.]],.],.],[.,[[[.,[.,.]],[.,[.,.]]],.]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[[[.,[.,.]],.],.],[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[[.,[.,.]],.],.],[.,[.,[[[.,[.,.]],[.,.]],.]]]]
[1,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0]=>[[[[.,[.,.]],.],[.,.]],[[[.,[[[.,.],.],.]],.],.]]
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[[[[.,[[[.,.],.],.]],[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[[[[.,[[[.,.],.],.]],.],.],[.,[[[.,[.,.]],.],.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[[[[.,[[[.,.],.],.]],.],.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[[[.,[.,.]],.],.]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,1,0]=>[[[[.,[[[.,.],.],[.,[.,[.,.]]]]],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[[[[.,[[[.,.],.],[.,.]]],.],.],[[[.,[.,.]],.],.]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[.,.]],[.,[[[[.,[.,.]],.],.],[[.,[.,.]],.]]]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[.,[[.,[.,.]],[[.,[[[.,.],.],.]],.]]]]
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[[[[.,[[[.,.],[.,.]],[.,[.,.]]]],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[.,[[[.,[[.,[.,.]],[[.,.],.]]],.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[.,[[[.,[.,.]],[.,.]],.]],.],.]]]
[1,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[.,[[[.,.],.],.]]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[[[[.,[[[.,.],[.,[.,[.,.]]]],.]],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0]=>[[[[.,[[[.,.],.],[.,.]]],.],.],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[[.,[.,.]],[.,[[.,[[[.,.],.],.]],[[.,[.,.]],.]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[.,[[[.,[.,.]],[.,[[[.,.],.],.]]],.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[[[[.,[[[.,.],[.,.]],.]],.],.],[[[.,[.,.]],.],.]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[.,.]],[.,[[[[[.,[.,.]],.],.],[.,[.,.]]],.]]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[.,[.,[[[[.,[.,.]],.],.],[[.,.],.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[.,[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[[[.,[[[.,.],[.,.]],.]],.],.],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[.,.]],[.,[[[.,[[[.,.],.],.]],[.,[.,.]]],.]]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[.,.]],[.,[.,[[.,[[[.,.],.],.]],[[.,.],.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[.,[.,.]],[.,[.,[[[[[.,[.,.]],.],.],[.,.]],.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[.,[.,[[[.,[[[.,.],.],.]],[.,.]],.]]]]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,0]=>[[[.,[.,.]],[.,[.,.]]],[[[[.,[.,.]],.],[.,.]],.]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],[.,[[[.,.],.],.]]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[[.,[[[.,.],.],.]],.],[.,.]],[.,[[[.,.],.],.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[[.,[.,.]],[.,[[[.,[.,.]],.],.]]],.],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[[.,[.,.]],[.,[.,[[[.,.],.],.]]]],.],[.,[.,.]]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[[.,[[[.,.],.],.]],[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[[.,[[[.,.],.],[.,.]]],[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[[[.,.],.],.]],[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[[[.,.],.],.]],[.,[[[.,[[[.,.],.],.]],.],.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[[.,[[[.,.],[.,.]],.]],[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[[[.,.],.],.]],[.,[[[.,[.,.]],[.,[.,.]]],.]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[[.,.],.],.]],[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[[.,.],.],.]],[.,[.,[[[.,[.,.]],[.,.]],.]]]]
[1,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,0]=>[[[.,[.,.]],[[.,.],.]],[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],[[[.,[.,.]],.],.]]
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[[[[.,[[[.,.],.],.]],[.,.]],.],[[[.,[.,.]],.],.]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[[.,[[[.,.],.],[.,[[[.,[.,.]],.],.]]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[[.,[[[.,.],.],[.,[.,[[[.,.],.],.]]]]],[.,[.,.]]]
[1,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0,1,0]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],[[[.,[.,.]],.],.]]
[1,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[[[.,[.,.]],.],[[.,[.,.]],.]],[.,[.,.]]]],.]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[[[.,[.,.]],.],.],[[.,[[[.,.],.],.]],.]]],.]
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],[[[.,[.,.]],.],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[[[.,[.,.]],.],.],[[.,[.,.]],[.,[.,.]]]]],.]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,[.,.]],[[.,[[.,[.,.]],[[.,.],.]]],.]]],.]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]],.]
[1,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,0]=>[[[[.,[.,.]],[.,.]],.],[[[.,[[[.,.],.],.]],.],.]]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[[.,[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,0]=>[[.,[[[.,.],.],[.,.]]],[[[.,[[[.,.],.],.]],.],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[[.,[[[[.,[[[.,.],.],.]],.],.],[[.,[.,.]],.]]],.]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[.,.]],[[.,[.,.]],[.,[[[.,.],.],.]]]]],.]
[1,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],[[[.,[.,.]],.],.]]],[.,[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[[[[.,[.,.]],.],.],[.,[.,.]]]]],.]
[1,1,0,0,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,[[[.,[[[[.,[.,.]],.],.],[[.,.],.]]],.],.]],.]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[[[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]],.],.]],.]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],[.,[[[.,.],.],.]]]],[.,[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,[[[.,.],.],.]],[.,[.,.]]]]],.]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[[[.,[[.,[[[.,.],.],.]],[[.,.],.]]],.],.]],.]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[.,[[[.,[[[[[.,[.,.]],.],.],[.,.]],.]],.],.]],.]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[[[.,[[[.,[[[.,.],.],.]],[.,.]],.]],.],.]],.]
[1,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[[[[.,[.,.]],.],[.,.]],.]]]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],[.,[[[.,.],.],.]]]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,0]=>[[[[.,[[[.,.],.],.]],[.,.]],.],[.,[[[.,.],.],.]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0,1,0]=>[[.,[[[.,.],[.,[[[.,[.,.]],.],.]]],.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,1,0,1,0,0]=>[[.,[[[.,.],[.,[.,[[[.,.],.],.]]]],.]],[.,[.,.]]]
[1,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,0]=>[[[[.,[.,.]],[.,[.,.]]],.],[[[.,[.,.]],[.,.]],.]]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0,1,0]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,0]=>[[.,[[.,[.,.]],[.,[.,.]]]],[[[[.,.],.],[.,.]],.]]
[1,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[[.,[[[[.,[.,.]],[[.,[.,.]],.]],.],[.,[.,.]]]],.]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[[.,.],.],.]],[[.,[[[.,.],.],.]],.]]],.]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],[.,[[[.,.],.],.]]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,[[[.,.],.],.]],[[.,[.,.]],[.,[.,.]]]]],.]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],[.,[[.,[.,.]],[[.,.],.]]]],.]],.]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[[.,[.,.]],[.,[[[.,[.,.]],[.,.]],.]]],.]],.]
[1,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,0]=>[[[[.,[.,.]],[[.,.],.]],.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0,1,0]=>[[.,[[[.,.],[.,[.,[.,.]]]],.]],[[[.,[.,.]],.],.]]
[1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,0]=>[[.,[[.,[.,.]],[[.,.],.]]],[.,[[[.,.],.],[.,.]]]]
[1,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,.],.],[[.,[.,.]],.]]],[.,[.,.]]]],.]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[[[[.,[.,.]],.],.],[.,[[[.,.],.],.]]],.]],.]
[1,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0]=>[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[[.,[[[[[.,[.,.]],.],[.,[.,.]]],[.,[.,.]]],.]],.]
[1,1,0,0,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[.,[[[[.,[.,.]],.],[[.,.],.]],[.,[.,.]]]]],.]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[.,[[[[.,[.,.]],.],.],[[.,[.,.]],[.,.]]]]],.]
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],.]],[[[.,[[[.,.],.],.]],.],.]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[[[[[.,[[[.,.],.],.]],.],.],[.,[.,.]]],.]],.]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[.,[[[[.,[[[.,.],.],.]],.],.],[[.,.],.]]]],.]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[.,[.,[[.,[.,.]],[[[[.,[.,.]],.],.],[.,.]]]]],.]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,[[.,[.,.]],[[.,[[[.,.],.],.]],[.,.]]]]],.]
[1,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[[[[.,[.,.]],[.,.]],.],[.,[[[.,[.,.]],[.,.]],.]]]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[[.,[[[.,.],[.,[.,[.,.]]]],.]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[[.,[[.,[.,.]],[.,.]]],[.,[[[[.,.],.],[.,.]],.]]]
[1,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,.],[[.,[.,.]],.]],.]],[.,[.,.]]]],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[[.,[[[.,.],.],.]],[.,[[[.,.],.],.]]],.]],.]
[1,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[[.,[[[.,[.,.]],[.,[.,.]]],.]],[[[.,.],[.,.]],.]]
[1,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[[.,[[[[[.,[.,.]],[.,[.,.]]],.],[.,[.,.]]],.]],.]
[1,1,0,0,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[.,[.,[[[[.,[.,.]],[[.,.],.]],.],[.,[.,.]]]]],.]
[1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[.,[.,[[.,[[[.,.],.],.]],[[.,[.,.]],[.,.]]]]],.]
[1,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[[.,[[[.,[.,.]],[[.,.],.]],.]],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[[.,[[[.,[[[.,.],.],[.,[.,.]]]],[.,[.,.]]],.]],.]
[1,1,0,0,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[.,[.,[[.,[[[.,.],.],[[.,.],.]]],[.,[.,.]]]]],.]
[1,1,0,0,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[[.,[.,[[[[[.,[.,.]],.],[.,.]],[.,[.,.]]],.]]],.]
[1,1,0,0,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[.,[.,[[[[[.,[[[.,.],.],.]],.],.],[.,.]],.]]],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[[.,[[[.,[[[.,.],[.,[.,.]]],.]],[.,[.,.]]],.]],.]
[1,1,0,0,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[.,[.,[[.,[[[.,.],[[.,.],.]],.]],[.,[.,.]]]]],.]
[1,1,0,0,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[[.,[.,[[[[[.,[.,.]],[.,.]],.],[.,[.,.]]],.]]],.]
[1,1,0,0,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[[.,[.,[[[.,[[[.,.],.],[.,.]]],[.,[.,.]]],.]]],.]
[1,1,0,0,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,[.,[[[.,[[[.,.],[.,.]],.]],[.,[.,.]]],.]]],.]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[[.,[.,.]],.],[[.,[.,[[.,.],.]]],.]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[[.,[.,.]],.],.],[[.,[.,[[.,[.,.]],[.,.]]]],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[[.,[.,.]],.],.],[[.,[[[.,[[.,.],.]],.],.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[.,[.,.]],[[.,[.,[[[[.,[.,.]],.],.],[.,.]]]],.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[[.,[.,[[.,[[[.,.],.],.]],[.,.]]]],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[[.,[.,.]],.],.],[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,.]],[[.,[[[.,[[.,[.,.]],[.,.]]],.],.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[.,.]],[[.,[[.,[.,.]],[[.,[[.,.],.]],.]]],.]]
[1,1,0,1,0,0,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[[[.,[.,[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]]],.],.]
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[.,[.,[[[[.,[[[.,.],.],.]],.],.],[.,.]]]],.],.]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,.]],[[.,[[[.,[.,.]],[.,[[.,.],.]]],.]],.]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[[[.,[.,[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]]],.],.]
[1,1,0,1,0,0,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[.,[.,[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]]],.],.]
[1,1,0,1,0,0,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[.,[.,[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]]],.],.]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[[[[.,[[[.,.],.],.]],.],.],[[.,[.,[[.,.],.]]],.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[[.,[.,.]],[[.,[.,.]],[.,[[[.,[[.,.],.]],.],.]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[[.,[[[.,[[[[.,[.,.]],.],.],[.,.]]],.],.]],.],.]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,[[[.,[[.,[[[.,.],.],.]],[.,.]]],.],.]],.],.]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[[.,[.,.]],[[[[.,[.,.]],.],.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,[[.,[.,.]],[[.,[[.,[.,.]],[.,.]]],.]]],.],.]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,[[[[.,[.,.]],.],.],[[.,[[.,.],.]],.]]],.],.]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[.,[.,[[[[.,[.,.]],.],[.,.]],[[[.,[.,.]],.],.]]]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[[.,[[[.,.],.],.]],.],[.,.]],[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,[[.,[.,.]],[[.,[.,.]],[.,[[.,.],.]]]]],.],.]
[1,0,1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[.,[.,[[[[.,[.,.]],[.,.]],[.,[.,.]]],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[.,[.,[[[[.,[[[.,.],.],[.,.]]],.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[[[[.,[[[.,.],[.,.]],.]],.],.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[[.,[.,.]],[[.,[[[.,.],.],.]],[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[[[.,[[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]],.]],.],.]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[[[.,[[.,[[[.,.],.],.]],[[.,[[.,.],.]],.]]],.],.]
[1,0,1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0]=>[.,[.,[[[[.,[.,.]],.],[.,.]],[.,[[[.,.],.],.]]]]]
[1,0,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[[.,[[[.,.],.],.]],[.,.]],.],[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[[[.,[[[[[.,[.,.]],.],.],[.,[[.,.],.]]],.]],.],.]
[1,0,1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[.,[.,[[[[.,[.,.]],[.,.]],.],[[[.,[.,.]],.],.]]]]
[1,0,1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[.,[.,[[.,[[[.,.],.],[.,.]]],[[[.,[.,.]],.],.]]]]
[1,0,1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[[.,[[[.,.],[.,.]],[.,[.,.]]]],[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[[[.,[[[.,[[[.,.],.],.]],[.,[[.,.],.]]],.]],.],.]
[1,0,1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>[.,[.,[[[[.,[.,.]],[.,.]],.],[.,[[[.,.],.],.]]]]]
[1,0,1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0]=>[.,[.,[[.,[[[.,.],.],[.,.]]],[.,[[[.,.],.],.]]]]]
[1,0,1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[.,[.,[[.,[[[.,.],[.,.]],.]],[[[.,[.,.]],.],.]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[[.,[.,.]],[[.,[.,[[.,.],.]]],.]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[.,[[[.,.],.],.]],[[.,[.,[[.,[.,.]],[.,.]]]],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],.],.]],[[.,[[[.,[[.,.],.]],.],.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[[.,[.,.]],[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,[.,.]],[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]],.]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[.,[[[.,.],.],.]],[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,[.,.]],[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]],.]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]],.]
[1,0,1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[.,[[[.,[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]],.],.]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[.,[[[.,[[[[.,[[[.,.],.],.]],.],.],[.,.]]],.],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]],.]
[1,0,1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[.,[[[.,[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]],.],.]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[.,[[[.,[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]],.],.]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[[.,[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]],.],.]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[[.,[[[.,.],.],[[.,[.,[[.,.],.]]],.]]],[.,[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[[[.,[.,.]],.],.],[.,[.,[[.,[.,.]],[.,.]]]]],.]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[[[.,[.,.]],.],.],[.,[[[.,[[.,.],.]],.],.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[.,[.,.]],[[.,[[[[.,[.,.]],.],.],[.,.]]],.]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[.,[.,.]],[[.,[[.,[[[.,.],.],.]],[.,.]]],.]]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[[[[[.,[.,.]],.],[.,[.,[[.,.],.]]]],[.,[.,.]]],.]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[.,[[[[.,[.,.]],.],.],[[.,[[.,[.,.]],[.,.]]],.]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[.,[[[[.,[.,.]],.],[[.,[[.,.],.]],.]],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[.,[[[[.,[.,.]],.],.],[[.,[.,.]],[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[[[[[.,[[[.,.],.],.]],.],.],[.,[.,[[.,.],.]]]],.]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[.,[[[[.,[[[.,.],.],.]],.],.],[[.,[[.,.],.]],.]]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[.,[[.,[.,.]],[[[[.,[.,.]],.],.],[.,[[.,.],.]]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[.,[[.,[.,.]],[[.,[[[.,.],.],.]],[.,[[.,.],.]]]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,1,1,0,0]=>[[.,[[[.,.],[[.,[.,[[.,.],.]]],.]],.]],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,[[[.,.],.],.]],[.,[.,[[.,[.,.]],[.,.]]]]],.]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,[[[.,.],.],.]],[.,[[[.,[[.,.],.]],.],.]]],.]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[[.,[.,.]],[.,[[[[.,[.,.]],.],.],[.,.]]]],.]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[[.,[.,.]],[.,[[.,[[[.,.],.],.]],[.,.]]]],.]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,1,1,0,0]=>[[[[[.,[.,.]],[.,[.,[[.,.],.]]]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[.,[[.,[[[.,.],.],.]],[[.,[[.,[.,.]],[.,.]]],.]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,0]=>[.,[[[[.,[.,.]],[[.,[[.,.],.]],.]],.],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[.,[[.,[[[.,.],.],.]],[[.,[.,.]],[.,[[.,.],.]]]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,1,1,0,0]=>[[[.,[[[.,.],.],[.,[.,[[.,.],.]]]]],[.,[.,.]]],.]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[.,[[[[[.,[.,.]],.],.],[.,[[.,[.,.]],[.,.]]]],.]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0]=>[.,[[.,[[[.,.],.],[[.,[[.,.],.]],.]]],[.,[.,.]]]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,0]=>[.,[[[[[.,[.,.]],.],[.,[[.,.],.]]],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[.,[[[[[.,[[[.,.],.],.]],.],.],[.,[[.,.],.]]],.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0]=>[[[.,[[[.,.],[.,[.,[[.,.],.]]]],.]],[.,[.,.]]],.]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,0]=>[.,[[.,[[[.,.],[[.,[[.,.],.]],.]],.]],[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,0]=>[.,[[[[[.,[.,.]],[.,[[.,.],.]]],.],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,0]=>[.,[[[.,[[[.,.],.],[.,[[.,.],.]]]],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[.,[[[.,[[[.,.],[.,[[.,.],.]]],.]],[.,[.,.]]],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]],.]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[[.,[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]],.]
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]],.]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]],.]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,[[.,.],.]],.]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]],.]
[1,1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]],.]
[1,1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.]],.]
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]],.]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]],.]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.]],.]
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]],.]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]],.]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]],.]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]],.]
[1,1,1,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]],.]
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[[.,[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]],.]
[1,1,1,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]],.]
[1,1,1,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,[[.,.],.]],.]]]
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]],.]
[1,1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],[[.,.],.]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]],.]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]]
[1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[[.,[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]],.]
[1,1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0,1,1,0,0,1,0,0]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],[[.,.],.]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]]
[1,1,1,0,0,1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]]
[1,1,1,0,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],[[.,.],.]]
[1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],[[.,.],.]]
[1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0,0,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,0,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]]
[1,1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]]
[1,1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]
[1,1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]
[1,1,1,1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]
[1,1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]
[1,1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[[.,[.,.]],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]
[1,1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[.,[.,.]],[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[.,[.,.]],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[.,[.,.]],[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[.,.]],[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[.,[.,.]],[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[.,.]],[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[.,[.,.]],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0,0,0]=>[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]]
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[[.,[[.,[.,.]],.]],.]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],[.,.]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[.,.]],.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],[.,.]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,[.,.]],.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[.,[[.,[.,.]],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]]
[1,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]]
[1,1,1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[[.,[[.,[.,.]],.]],.]]
[1,1,1,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0,0,0]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]]
[1,0,1,1,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]]
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0,0,0]=>[.,[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],.]]
[1,1,1,0,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],[.,.]]
[1,0,1,1,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]]
[1,0,1,1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[.,[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],.]]
[1,0,1,1,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0,0,0]=>[.,[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],.]]
[1,1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],[.,.]]
[1,0,1,1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]]
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[.,[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],.]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],[.,.]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[.,[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[.,[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],[.,.]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[.,[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],.]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[.,[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[.,[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],[.,.]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[[[.,[.,.]],[.,.]],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[[.,[[.,[.,.]],.]],.]]
[1,1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0,0,0]=>[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],[.,.]]
[1,0,1,1,0,1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]]
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0,0,0]=>[.,[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],.]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],[.,.]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[.,[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[.,[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],.]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],[.,.]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[.,[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],.]]
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],[.,.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]]
[1,0,1,1,0,0,1,1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[.,[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],.]]
[1,0,1,1,0,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[.,[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],.]]
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],[.,.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[.,[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],.]]
[1,0,1,1,0,0,1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[.,[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[.,[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],.]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],[.,.]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[.,[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[.,[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],.]]
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],[.,.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]]
[1,0,1,1,0,0,1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[.,[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[.,[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],[.,.]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[.,[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[.,[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],[.,.]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[.,[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[.,[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],.]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[[.,[.,.]],.],[[.,[.,.]],.]],[.,.]],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,.]],.],[[.,[.,[[.,[.,.]],.]]],.]],[.,.]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[.,[[[.,[.,.]],.],[[.,[.,.]],.]]],.],.],[.,.]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[[[.,[[[[.,.],.],[[.,[.,.]],.]],.]],.],.],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[[[.,.],[[.,[.,.]],.]],.]],[.,.]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[.,[[.,[.,.]],.]],.],.],[[.,[[.,[.,.]],.]],.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],.],[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[.,.]],[[[[.,[.,.]],.],[[.,[.,.]],.]],[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[.,[.,.]],[[.,[[.,.],[[.,[[.,[.,.]],.]],.]]],.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[.,[.,[[[.,.],[[.,.],.]],.]]],.]]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[.,[.,.]],[[[[[.,.],.],[[.,[.,.]],.]],.],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[[.,[.,.]],[[.,[[[.,[.,.]],.],[.,[.,.]]]],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[[.,[.,.]],[[.,[[[[.,.],.],[.,[.,.]]],.]],[.,.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[[.,[.,[[.,[.,.]],.]]],.],[[.,[.,.]],.]],[.,.]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[[.,[[.,[.,.]],.]],.],.],[[.,.],[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[.,.]],.],[[[.,.],[[.,[[.,[.,.]],.]],.]],.]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[.,[.,.]],[[.,.],[[.,[[.,.],[[.,[.,.]],.]]],.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[.,.],[[.,[[[.,.],[[.,.],.]],.]],.]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],.],[[[[.,[.,.]],.],[[.,[.,.]],.]],.]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[.,[.,.]],[[[.,[.,.]],.],[[.,[[.,[.,.]],.]],.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,.],[[.,[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[[.,[.,.]],.],[[.,[[.,[.,.]],.]],.]]],.],.]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],.],[[[.,.],[[.,.],.]],.]]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[.,[[[.,[.,.]],.],[[.,.],[[.,[.,.]],.]]]],.],.]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,[[.,.],[[.,[[.,.],[[.,[.,.]],.]]],.]]],.],.]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[[.,[[.,.],[[.,[[[.,.],[[.,.],.]],.]],.]]],.],.]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[[.,[.,.]],.],[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],[.,[[.,[.,.]],.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[.,.],[[.,[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]],.]]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[[.,[[[[[.,.],.],[[.,[.,.]],.]],.],[.,.]]],.],.]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,[[.,[.,.]],.]],[.,[[.,[.,.]],.]]]],.],.]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[.,[[[[.,[.,.]],.],[[.,.],.]],.]]],.]]
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[[[.,[[.,[[[.,[.,.]],.],[.,[.,.]]]],[.,.]]],.],.]
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,[[[[[.,[.,.]],.],[[.,.],.]],[.,.]],.]],.],.]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[.,[[[[.,[.,.]],.],[[.,.],[[.,.],.]]],.]],.],.]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[.,.],[[.,[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]],.]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[[[.,[[.,[[[[.,.],.],[.,[.,.]]],.]],[.,.]]],.],.]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[[[.,[[[[[[.,.],.],[[.,.],.]],.],[.,.]],.]],.],.]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[[[.,[[[.,[[[.,[.,.]],.],[.,.]]],[.,.]],.]],.],.]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[.,[[[.,[[[[.,.],.],[.,.]],.]],[.,.]],.]],.],.]
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,[[[.,[.,.]],.],.]]]
[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[[[[[.,.],.],[[.,[.,.]],.]],[.,.]],.],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],.],[[.,[.,[[.,[.,.]],.]]],.]],.],[.,.]]
[1,1,1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[[.,[[[.,[[[.,[.,.]],.],[.,[.,.]]]],.],.]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[[.,[[[.,[[[[.,.],.],[.,[.,.]]],.]],.],.]],[.,.]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[[[[[.,.],.],[[[.,.],[[.,[.,.]],.]],.]],.],[.,.]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[.,[[[.,[[.,[.,.]],.]],.],.]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[.,[[.,[.,.]],.]],[.,[.,[[.,.],[[.,[.,.]],.]]]]]
[1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],[[[[.,[.,.]],.],[[.,.],.]],[.,.]]],.]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,.],[[.,[[.,.],[[.,[[.,[.,.]],.]],.]]],.]],.]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[.,[.,[[[.,.],[[.,.],.]],.]]]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[[[.,[.,.]],[[[[[.,.],.],[[.,.],.]],.],[.,.]]],.]
[1,1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[[[.,[.,.]],[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]],.]
[1,1,0,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[.,[.,.]],[[.,[[[[.,.],.],[.,.]],.]],[.,.]]],.]
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[[[[[.,.],.],[[.,[.,.]],.]],.],[[[.,[.,.]],.],.]]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[[.,[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[[.,[[[.,[.,.]],.],[.,[.,[[.,[.,.]],.]]]]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[.,[[[.,[.,.]],.],[[.,.],.]]],.],.],[.,.]],.]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[[[[[.,[[[[.,.],.],[[.,.],.]],.]],.],.],[.,.]],.]
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[[.,[[[.,[.,.]],.],[.,[.,.]]]],[[[.,[.,.]],.],.]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[[.,[.,.]],.],[[.,.],.]],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[.,[[[[.,[.,.]],.],[[.,[[.,[.,.]],.]],.]],[.,.]]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[[[[[.,[.,.]],.],[[[.,.],[[.,.],.]],.]],[.,.]],.]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[.,[[[[.,[.,.]],.],[[.,.],[[.,[.,.]],.]]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[.,[[[.,[.,.]],.],[[.,[[.,.],[[.,[.,.]],.]]],.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[.,[[[.,[.,.]],.],[[.,[[[.,.],[[.,.],.]],.]],.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[[[.,[.,[[.,[.,.]],.]]],.],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[[.,[[.,[.,.]],.]],.],.],[[.,.],[[.,.],.]]],.]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[[[[[.,[.,[[.,[.,.]],.]]],.],[[.,.],.]],[.,.]],.]
[1,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[.,[[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[.,[[[.,[.,.]],.],[[.,.],[[.,[[.,[.,.]],.]],.]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],.],[[[[.,[.,.]],.],[[.,.],.]],.]],.]
[1,0,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[.,[[[.,[.,.]],.],[[[.,[.,.]],.],[[.,[.,.]],.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[.,[[.,.],[[.,[[[.,[.,.]],.],[[.,[.,.]],.]]],.]]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[.,[.,.]],[[[.,[.,.]],.],[[.,.],[[.,.],.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[[[.,[.,.]],.],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[.,[[[.,[.,.]],.],[[.,[[.,[.,.]],.]],[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[.,[[.,.],[[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]],.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,.],[[.,[[[[.,[.,.]],.],[[.,.],.]],.]],.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0]=>[[[[.,.],[[.,[.,.]],.]],.],[.,[[[.,[.,.]],.],.]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0,0,0,1,0]=>[[.,[[[[[.,.],.],[.,[.,.]]],[.,.]],.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[[.,[[[[.,.],.],[.,[.,[[.,[.,.]],.]]]],.]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[[[.,[[[.,[[[.,[.,.]],.],[.,.]]],.],.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[.,[[[.,[[[[.,.],.],[.,.]],.]],.],.]],[.,.]],.]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,[[[.,[.,.]],.],.]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0,0,1,0,0]=>[[[[[[[.,.],.],[[.,.],.]],[.,.]],.],[.,[.,.]]],.]
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[[.,.],.]],[.,[[[.,[.,.]],.],.]]],.]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[.,[[[[[.,.],.],[[.,[[.,[.,.]],.]],.]],.],[.,.]]]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[[[[[[.,.],.],[[[.,.],[[.,.],.]],.]],.],[.,.]],.]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[.,[[[[[.,.],.],[[.,.],[[.,[.,.]],.]]],.],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[.,[[.,[[.,[.,.]],.]],[.,[[.,.],[[.,[.,.]],.]]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[.,[[.,[[.,[.,.]],.]],[.,[[[.,.],[[.,.],.]],.]]]]
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0]=>[[.,[[[[.,.],.],[.,[.,.]]],.]],[[[.,[.,.]],.],.]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0,0,0]=>[[[.,[[[[.,[.,.]],.],[.,.]],[.,.]]],[.,[.,.]]],.]
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[[[[[[.,.],.],[[.,.],.]],.],[[[.,[.,.]],.],.]],.]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[.,[[.,[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]],[.,.]]]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[[[.,[[[.,[.,.]],.],[.,.]]],[[[.,[.,.]],.],.]],.]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[[.,[.,.]],.],[[.,.],[[.,.],.]]],[.,.]],.]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[[[.,[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]],[.,.]],.]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[.,[[.,[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]],[.,.]]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[[[[.,[[.,[.,.]],.]],.],[[.,.],.]],[.,.]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],.],[[[.,[.,.]],.],[[.,.],.]]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[[[.,[.,.]],.],[[.,[[.,[.,.]],.]],[.,.]]],.]]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,[[[.,[.,.]],.],.]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0,0,0]=>[[[.,[[[[[.,.],.],[.,.]],[.,.]],.]],[.,[.,.]]],.]
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>[[[[[.,.],[[.,.],.]],.],[.,[[[.,[.,.]],.],.]]],.]
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0]=>[.,[[.,[[[[.,.],.],[.,[[.,[.,.]],.]]],.]],[.,.]]]
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[[[.,[[.,[.,.]],[.,.]]],[.,[[[.,[.,.]],.],.]]],.]
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0,0]=>[.,[[[[[[.,.],.],[[.,.],[[.,.],.]]],.],[.,.]],.]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[[[.,[[[[.,.],.],[.,.]],.]],[[[.,[.,.]],.],.]],.]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,0]=>[.,[[[.,[[[.,[[.,[.,.]],.]],.],[.,.]]],[.,.]],.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0]=>[[[.,[[[.,.],[.,.]],.]],[.,[[[.,[.,.]],.],.]]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[.,[[.,[[.,[[.,[[.,[[.,.],.]],[.,.]]],.]],.]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[.,[[.,[[.,[[.,[[.,.],.]],[.,[[.,.],.]]]],.]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],[.,.]]],.]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[.,[[.,[[[[.,[.,.]],[.,.]],.],[.,.]]],.]],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,[[.,.],.]],[[[.,.],[.,[[.,.],.]]],.]]],.]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[[.,[.,.]],[[.,[[.,.],.]],.]],.],[.,.]]],.]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[.,[[.,[[.,[[.,.],.]],[.,[[.,[[.,.],.]],.]]]],.]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[.,[[.,[[.,[[.,.],.]],[.,[[[.,.],[.,.]],.]]]],.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[[[.,.],[.,[[.,[[.,.],.]],[[.,.],.]]]],.]],.]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[.,[[.,[[.,[[.,[[.,.],.]],.]],[.,[[.,.],.]]]],.]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,.]]],.]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[.,[[[.,.],[[[[.,.],[.,[.,.]]],.],[.,.]]],.]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[.,[[[.,.],[[[[.,[.,.]],[.,.]],.],[.,.]]],.]],.]
[1,0,1,1,0,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[.,[[.,[[[[.,[.,.]],[.,[[.,.],.]]],.],[.,.]]],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,[[.,.],.]],[[.,[[[.,.],[.,.]],.]],.]]],.]
[1,0,1,1,0,0,1,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[.,[[.,[[[[.,[.,[[.,.],.]]],[.,.]],.],[.,.]]],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[[.,[[.,.],.]],[[[.,.],[[.,.],[.,.]]],.]]],.]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[[.,[[.,.],.]],[[[.,[[.,.],.]],[.,.]],.]]],.]
[1,0,1,1,0,0,1,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[.,[[.,[[[[[.,[.,.]],[.,.]],[.,.]],.],[.,.]]],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],[[[.,.],[.,.]],.]]],.]
[1,1,0,0,1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[[.,[[.,[[.,[[[.,.],[[.,.],.]],.]],.]],[.,.]]],.]
[1,0,1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,0]=>[.,[[.,[[[[.,[.,.]],.],[.,.]],[.,[[.,.],.]]]],.]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0]=>[[.,[[[[.,[.,.]],[[[.,.],[.,.]],.]],.],[.,.]]],.]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0]=>[[.,[[[[.,[.,[[.,.],.]]],[[.,.],.]],.],[.,.]]],.]
[1,1,0,0,1,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0]=>[[.,[[[[[.,[.,.]],[[.,.],.]],[.,.]],.],[.,.]]],.]
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[[[[.,[.,.]],.],[[.,.],.]],[.,[[.,.],.]]]],.]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,[[.,.],.]],[.,[.,[[.,[[.,.],.]],.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[[.,.],[.,[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],.]],[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,1,0,0]=>[[.,.],[[[[.,[.,.]],[.,[.,[[.,.],.]]]],.],[.,.]]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[[.,.],[[.,[[.,.],.]],[.,[.,[[[.,.],[.,.]],.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[[.,.],[.,[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[.,.],[.,[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]]],.]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0,1,0]=>[[.,.],[[[[.,[.,[[.,.],.]]],[.,[.,.]]],.],[.,.]]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,0,1,0]=>[[.,.],[[[[[.,[.,.]],[.,[.,.]]],[.,.]],.],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0]=>[[.,.],[[[[.,[.,.]],.],[.,[.,.]]],[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[[.,.],[[.,.],[.,[.,[[.,[[.,.],.]],[.,.]]]]]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,0,1,0]=>[[.,.],[[[[.,[.,.]],[[.,.],[.,[.,.]]]],.],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[[.,.],[[.,.],[[[[.,.],[.,[.,.]]],.],[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[.,.],[[.,.],[[[[.,[.,.]],[.,.]],.],[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[[[.,.],[[[[.,.],[.,[.,[[.,.],.]]]],.],[.,.]]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[[[.,.],[[.,.],[.,[.,.]]]],.],[.,.]]],.]
[1,1,0,1,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[[[.,.],[[[[[.,.],[.,[.,.]]],[.,.]],.],[.,.]]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[[.,[[[.,.],[[.,.],.]],.]],.]],[.,.]]]
[1,1,0,1,1,0,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0]=>[[[.,.],[[[[.,.],.],[.,[.,.]]],[.,[[.,.],.]]]],.]
[1,1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[[[.,.],[[[[.,[.,.]],[[.,.],[.,.]]],.],[.,.]]],.]
[1,1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[[[.,.],[[[[.,[.,[[.,.],.]]],[.,.]],.],[.,.]]],.]
[1,1,0,1,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[[[.,.],[[[[[.,[.,.]],[.,.]],[.,.]],.],[.,.]]],.]
[1,1,0,1,1,0,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,0]=>[[[.,.],[[[[.,[.,.]],.],[.,.]],[.,[[.,.],.]]]],.]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,.],.]],.],[[.,[.,[[.,[[.,.],.]],.]]],.]]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[[.,.],[[.,[.,[[.,.],.]]],.]],.]],.],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[.,[[.,.],.]],[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]]
[1,1,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0,0,1,0]=>[[[.,[[[[.,.],[[.,[.,.]],.]],[.,.]],.]],.],[.,.]]
[1,1,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,1,0]=>[[[.,[[[.,.],.],[[.,[.,.]],.]]],.],[.,[[.,.],.]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,[[.,.],.]],.],[[[.,.],[.,[.,[[.,.],.]]]],.]]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0,0,1,0]=>[[[.,[[[.,.],[[[.,.],[.,[.,.]]],.]],.]],.],[.,.]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[[.,[[.,.],.]],.],[[[.,.],[[.,.],[.,[.,.]]]],.]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[[.,.],[[.,.],[[.,.],[.,.]]]],.]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[.,[[.,.],.]],[[[.,.],[[.,[[.,.],.]],[.,.]]],.]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[.,[[.,.],.]],[[[[[.,.],[.,[.,.]]],.],[.,.]],.]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[[.,[[.,.],.]],[[.,.],[.,.]]],.]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[.,[[.,.],.]],[[[.,[[.,[[.,.],.]],.]],[.,.]],.]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[.,[[.,.],.]],[[[[[.,[.,.]],[.,.]],.],[.,.]],.]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[.,[[.,.],.]],.]],.],[[.,[.,[[.,.],.]]],.]]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0,0,1,0]=>[[[.,[[[.,[[.,.],.]],[[.,[.,.]],.]],.]],.],[.,.]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[[[.,[[.,[[.,.],.]],.]],.],[[[.,.],[.,[.,.]]],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[[.,[[.,.],.]],.]],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[[.,[[.,.],.]],.]],[[[.,[[.,.],.]],[.,.]],.]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[[[.,[[.,[[.,[[.,.],.]],.]],.]],.],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],[[[.,.],[.,.]],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[[.,[[.,[[.,[[[.,.],[[.,.],.]],.]],.]],.]],[.,.]]
[1,1,1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,.],[[.,[.,.]],.]]],.]],[.,[[.,.],.]]]
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[[.,[[.,[[[.,.],[[[.,.],[.,.]],.]],.]],.]],[.,.]]
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[[.,[[.,[[[.,[[.,.],.]],[[.,.],.]],.]],.]],[.,.]]
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[[.,[[.,[[[[.,.],[[.,.],.]],[.,.]],.]],.]],[.,.]]
[1,1,1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0]=>[[.,[[.,[[[.,.],.],[[.,.],.]]],.]],[.,[[.,.],.]]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[[.,[.,.]],[[.,[.,[[.,.],.]]],.]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,0,1,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],[.,[[.,.],.]]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[[[[.,[.,.]],[[[.,.],[.,[.,.]]],.]],[.,.]],[.,.]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[[[[.,[.,.]],[[[.,.],[[.,.],[.,.]]],.]],.],[.,.]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[[.,[.,.]],[[[.,[[.,.],.]],[.,.]],.]],.],[.,.]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[[[[.,[.,[[.,.],.]]],[[.,[.,.]],.]],[.,.]],[.,.]]
[1,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[[[[.,[.,[[.,.],.]]],[[[.,.],[.,.]],.]],.],[.,.]]
[1,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[[[[.,[.,[[.,[[.,.],.]],.]]],[[.,.],.]],.],[.,.]]
[1,1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[[[[.,[.,[[[.,.],[[.,.],.]],.]]],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0]=>[[[[[.,[.,.]],[[[.,.],[.,.]],.]],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0]=>[[[[[.,[.,[[.,.],.]]],[[.,.],.]],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0]=>[[[[[[.,[.,.]],[[.,.],.]],[.,.]],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,0]=>[[[[[.,[.,.]],[[.,.],.]],[.,[[.,.],.]]],.],[.,.]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[[.,[.,.]],.]],[[.,[[.,.],.]],.]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[[[[.,[.,.]],.],[[[.,.],[.,.]],.]],[.,[[.,.],.]]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[[[[.,[.,[[.,.],.]]],.],[[.,.],.]],[.,[[.,.],.]]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[[[[[.,[.,.]],[[.,.],.]],.],[.,.]],[.,[[.,.],.]]]
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],.],[[.,.],.]],[.,[[.,[[.,.],.]],.]]]
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[[[.,[.,.]],.],[[.,.],.]],.]]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[[.,[.,.]],[[.,[[.,.],[.,.]]],.]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],[.,.]],[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0,0,0,0,0]=>[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0]=>[[[.,[.,.]],[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[.,[[.,[[.,.],[.,.]]],.]]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,[.,.]],[[.,[[[.,.],[.,.]],[.,.]]],.]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[[.,[[.,[[.,.],[.,.]]],.]],.]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0]=>[[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]]
[1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[[[.,[.,.]],[[.,.],[.,.]]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0]=>[[[.,[.,.]],[[.,.],[.,.]]],[[.,[[.,.],[.,.]]],.]]
[1,1,1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]],[.,.]]
[1,1,1,1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[[.,[.,.]],[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[[.,[.,.]],[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]=>[[.,[.,.]],[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[[.,[.,.]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[[.,[.,.]],[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]]]
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[.,[[.,[[.,.],[.,.]]],.]]],[.,.]]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[[[.,[.,.]],[[.,[[.,.],[.,.]]],.]],[[.,.],[.,.]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]]
[1,1,1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[.,[.,.]],[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,[.,.]],[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]]
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[.,[.,.]],[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[[[[[.,[[.,[.,.]],[.,.]]],.],[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[.,.]],[.,.]]
[1,1,1,1,1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[[[.,[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]],.],[.,.]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[.,[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]],.],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[[[.,[[.,.],[.,.]]],.],[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,0,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0]=>[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[.,.],[.,.]]]
[1,1,1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[[[.,[[.,.],[.,.]]],.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[.,[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]],.]
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0]=>[[.,[[.,.],[.,.]]],[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[[[.,[[.,.],[.,.]]],.],[.,[[.,[[.,.],[.,.]]],.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[.,[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]]],.]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[[.,[.,.]],[[.,[[[.,.],[.,.]],[.,.]]],.]]],.]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[.,[[.,[.,.]],[[.,[[.,[[.,.],[.,.]]],.]],.]]],.]
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[[[[.,[[[.,[.,.]],[.,.]],[.,.]]],.],[.,.]],[.,.]]
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[[[.,[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]],.],[.,.]]
[1,1,1,1,0,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]],.]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[[.,[.,.]],[[.,[[.,.],[.,.]]],.]],[.,.]]],.]
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[[.,[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]],.]
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]],.]
[1,0,1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[.,[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[.,[[[[.,.],[.,.]],[.,.]],[.,[[.,.],[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[.,[[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0]=>[.,[[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]]]
[1,0,1,1,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[.,[[[[.,.],[.,.]],[.,.]],[[.,[[.,.],[.,.]]],.]]]
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[[.,[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.],[.,.]]
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0]=>[[.,[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]],.]
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[.,[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[.,.]]],.]
[1,0,1,1,1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[.,[[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[[.,[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]],.]]
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],[.,[[.,[[.,.],[.,.]]],.]]]],.]
[1,0,1,1,1,1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[.,[[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]],[.,.]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]]]
[1,0,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[[.,[[[.,.],[.,.]],[.,.]]],.]]]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[[.,[[.,[[.,.],[.,.]]],.]],.]]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[[[[.,[[.,[[.,[.,.]],[.,.]]],.]],.],[.,.]],[.,.]]
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[[[.,[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]],.],[.,.]]
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[[.,[[.,[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]],.]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[.,[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]],.]],.]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[[[.,[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]],.],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[[.,[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[.,.]]],.]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[[.,[[[[.,[[.,[.,.]],[.,.]]],.],[.,.]],[.,.]]],.]
[1,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,0,0,0]=>[.,[[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[.,[[[.,[[.,.],[.,.]]],.],[.,[[.,.],[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]]
[1,0,1,1,1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],[[.,[[.,.],[.,.]]],.]]]
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[[[.,[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[[.,[[.,[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[[.,[[[.,[[[.,[.,.]],[.,.]],[.,.]]],.],[.,.]]],.]
[1,0,1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[.,[[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]],[.,.]]]
[1,0,1,1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.]],.]
[1,0,1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[.,[[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.],[.,.]]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[.,[[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]],.]]
[1,0,1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[.,[[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]],.]]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[.,[[.,[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.]],.]
[1,0,1,1,1,1,0,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.],[.,.]]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]],.]]
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[.,[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.]]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[.,[[.,[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]]],.]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[[[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[.,[[.,[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[[.,[[[.,[[.,[[.,[.,.]],[.,.]]],.]],.],[.,.]]],.]
[1,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[.,[[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]],[.,.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[[.,[[.,[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]],.]],.]
[1,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0,0]=>[.,[[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.],[.,.]]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0,0]=>[.,[[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]],.]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]],.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[.,[[.,[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]],.]],.]
[1,0,1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[.,[[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.],[.,.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[.,[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[.,[[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[.,[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]],.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]],.]],.]
[1,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[.,[[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.],[.,.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[.,[[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[.,[[.,[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[.,[[.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]],.]]
[1,1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[.,.],[[[[.,.],[.,.]],[[.,.],.]],[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]=>[[[[.,.],[.,.]],[[.,.],[[.,.],.]]],[[.,.],[.,.]]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]=>[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[.,[[[[.,.],[.,.]],[[.,.],.]],[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[.,[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[[.,[.,[.,[.,.]]]],.],[[.,[.,.]],.]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,0,0,0,1,0]=>[[[[[.,.],.],.],[.,[.,.]]],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[[[[[.,[.,[.,.]]],.],.],[.,[.,.]]],[[[.,.],.],.]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0]=>[[[[.,.],[.,.]],[[[.,.],.],.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.],.]
[1,1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[[[[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],.]]],.],.]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0,0]=>[[[[[.,.],[.,.]],[.,.]],[[.,.],[[[.,.],.],.]]],.]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]]
[1,0,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[.,[.,[[[[.,.],[.,.]],[[.,.],.]],[[.,.],[.,.]]]]]
[1,1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],[[[.,.],.],.]]],[[.,.],[.,.]]]
[1,1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]=>[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],[[[.,.],.],[.,.]]]
[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0]=>[[[[.,.],[.,.]],[[.,[.,.]],[.,.]]],[[[.,.],.],[.,.]]]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[[[.,[.,.]],.],[[.,.],.]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[[[.,[.,.]],.],[[.,[.,.]],[.,.]]],[[[.,[.,.]],.],.]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[[.,[[[.,.],.],.]],.],[[.,.],.]],[[[.,[.,.]],.],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[[.,[.,.]],.],[[[[.,[.,.]],.],.],[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[[.,[.,.]],.],[[.,[[[.,.],.],.]],[.,.]]],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[[.,.],.]],[.,[.,.]]],[[[.,[.,.]],.],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[[[.,[[[.,.],.],.]],.],[[.,[.,.]],[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[[.,[[[.,.],.],[[.,.],.]]],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[[[[.,[.,.]],.],.],[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[[.,[.,.]],.],.],[[[[.,[[[.,.],.],.]],.],.],[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[[.,[[[.,.],[[.,.],.]],.]],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[[[[.,[.,.]],.],.],[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[[.,[.,.]],.],.],[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[[.,[.,.]],.],.],[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]]
[1,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],.],[[.,.],.]],[[[.,[[[.,.],.],.]],.],.]]
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[[[[.,[.,.]],[[.,[.,.]],[.,.]]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[[.,[[[.,.],.],.]],[[.,.],.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[[.,[[[.,.],.],.]],.],.],[[[[.,[.,.]],.],.],[.,.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[[.,[[[.,.],.],.]],.],.],[[.,[[[.,.],.],.]],[.,.]]]
[1,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[[.,.],.]],[[[.,[.,.]],.],.]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[[[[.,[[[.,.],.],[[.,[.,.]],[.,.]]]],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[[[[.,[[[.,.],.],[[.,.],.]]],.],.],[[[.,[.,.]],.],.]]
[1,1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[[.,[.,.]],[[[[.,[.,.]],.],[.,.]],[[[.,[.,.]],.],.]]]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[[[[.,[[[.,.],.],.]],.],[.,.]],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[[.,[[[.,.],[[.,.],.]],[.,[.,.]]]],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,[.,.]]],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[[.,[.,.]],[[[[.,[[[.,.],.],[.,.]]],.],.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,[.,.]],[[[[.,[[[.,.],[.,.]],.]],.],.],[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[[.,.],.]],[.,[[[.,.],.],.]]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]=>[[[[.,[[[.,.],[[.,[.,.]],[.,.]]],.]],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[[[[.,[[[.,.],.],[[.,.],.]]],.],.],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0]=>[[.,[.,.]],[[[[.,[.,.]],.],[.,.]],[.,[[[.,.],.],.]]]]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[[[[.,[[[.,.],.],.]],[.,.]],.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>[[[[.,[[[.,.],[[.,.],.]],.]],.],.],[[[.,[.,.]],.],.]]
[1,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[[.,[.,.]],[[[[.,[.,.]],[.,.]],.],[[[.,[.,.]],.],.]]]
[1,1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[[.,[.,.]],[[.,[[[.,.],.],[.,.]]],[[[.,[.,.]],.],.]]]
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[[.,[.,.]],[[.,[[[.,.],[.,.]],[.,[.,.]]]],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[[[[.,[[[.,.],[[.,.],.]],.]],.],.],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>[[.,[.,.]],[[[[.,[.,.]],[.,.]],.],[.,[[[.,.],.],.]]]]
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0]=>[[.,[.,.]],[[.,[[[.,.],.],[.,.]]],[.,[[[.,.],.],.]]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[[.,[.,.]],[[.,[[[.,.],[.,.]],.]],[[[.,[.,.]],.],.]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[.,[.,.]],[[.,[[[.,.],[.,.]],.]],[.,[[[.,.],.],.]]]]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],[.,[.,.]]],[[[[.,[.,.]],.],[[.,.],.]],.]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[[[.,[.,.]],.],[[.,[.,.]],[.,.]]],[.,[[[.,.],.],.]]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[[.,[[[.,.],.],.]],.],[[.,.],.]],[.,[[[.,.],.],.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[[.,[.,.]],[[[[.,[.,.]],.],.],[.,.]]],.],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[[.,[.,.]],[[.,[[[.,.],.],.]],[.,.]]],.],[.,[.,.]]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[[.,.],.]],[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[[[.,[[[.,.],.],.]],[[.,[.,.]],[.,.]]],.],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[[.,[[[.,.],.],[[.,.],.]]],[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[[.,[[[.,.],.],.]],[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[.,[[[.,.],.],.]],[[[[.,[[[.,.],.],.]],.],.],[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[[.,[[[.,.],[[.,.],.]],.]],[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[[.,[[[.,.],.],.]],[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[[.,[[[.,.],.],.]],[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,[[[.,.],.],.]],[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]]
[1,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],[[.,.],.]],[.,[[[.,[.,.]],.],[[.,.],.]]]]
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[[[[.,[.,.]],[[.,[.,.]],[.,.]]],.],[[[.,[.,.]],.],.]]
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[[.,[[[.,.],.],.]],[[.,.],.]],.],[[[.,[.,.]],.],.]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[.,[[[.,.],.],[[[[.,[.,.]],.],.],[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[[[.,.],.],[[.,[[[.,.],.],.]],[.,.]]]],[.,[.,.]]]
[1,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],.],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[[.,[[[.,.],.],[[.,[.,.]],[.,.]]]],[[[.,[.,.]],.],.]]
[1,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],[[[.,[.,.]],.],[.,.]]],.]
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[[[.,[[[.,.],.],.]],.],[.,.]],[[[.,[.,.]],.],.]],.]
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[[.,[[[.,.],[[.,.],.]],[.,[.,.]]]],[[[.,[.,.]],.],.]]
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[[[[[.,[.,.]],[.,.]],[.,[.,.]]],[[[.,[.,.]],.],.]],.]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[[[.,[[[.,.],.],[.,.]]],.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[[[.,[[[.,.],[.,.]],.]],.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[[.,.],.]],.],[[[.,[[[.,.],.],.]],.],.]]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]=>[[.,[[[.,.],[[.,[.,.]],[.,.]]],[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[[.,[[[.,.],.],[[.,.],.]]],[[[.,[[[.,.],.],.]],.],.]]
[1,1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0]=>[[[[[.,[.,.]],.],[.,.]],[[[.,[[[.,.],.],.]],.],.]],.]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[[[[[.,[[[.,.],.],.]],[.,.]],[.,[.,.]]],[.,[.,.]]],.]
[1,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>[[.,[[[.,.],[[.,.],.]],[[[.,[.,.]],.],.]]],[.,[.,.]]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[[[[[.,[.,.]],[.,.]],[[[.,[.,.]],.],.]],[.,[.,.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[[[[[.,[[[.,.],.],[.,.]]],.],.],[[[.,[.,.]],.],.]],.]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[[[[[.,[[[.,.],[.,.]],[.,[.,.]]]],.],.],[.,[.,.]]],.]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[[.,[[[.,.],[[.,.],.]],[.,[[[.,.],.],.]]]],[.,[.,.]]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>[[[[[.,[.,.]],[.,.]],[.,[[[.,.],.],.]]],[.,[.,.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0]=>[[[[[.,[[[.,.],.],[.,.]]],.],.],[.,[[[.,.],.],.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[[[[[.,[[[.,.],[.,.]],.]],.],.],[[[.,[.,.]],.],.]],.]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[[[[.,[[[.,.],[.,.]],.]],.],.],[.,[[[.,.],.],.]]],.]
[1,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[.,[[[[.,[.,.]],.],[[.,.],.]],.]]]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[[[[.,[.,.]],[[.,[.,.]],[.,.]]],.],[.,[[[.,.],.],.]]]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[[.,[[[.,.],.],.]],[[.,.],.]],.],[.,[[[.,.],.],.]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[.,[[[.,.],[[[[.,[.,.]],.],.],[.,.]]],.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[[[.,.],[[.,[[[.,.],.],.]],[.,.]]],.]],[.,[.,.]]]
[1,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[.,[.,.]]],.],[[[.,[.,.]],[[.,.],.]],.]]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[[.,[[[.,.],.],[[.,[.,.]],[.,.]]]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0,0]=>[[.,[[.,[.,.]],[.,[.,.]]]],[[[[.,.],.],[[.,.],.]],.]]
[1,1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,0]=>[[[[.,[.,.]],[.,[.,.]]],[[[[.,[.,.]],.],[.,.]],.]],.]
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[[[.,[[[.,.],.],.]],.],[.,.]],[.,[[[.,.],.],.]]],.]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[[.,[[[.,.],[[.,.],.]],[.,[.,.]]]],[.,[[[.,.],.],.]]]
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[[[[[.,[.,.]],[.,.]],[.,[.,.]]],[.,[[[.,.],.],.]]],.]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[[[.,[[[.,.],.],[.,.]]],[.,[.,.]]],.],[.,[.,.]]],.]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[[[.,[[[.,.],[.,.]],.]],[.,[.,.]]],.],[.,[.,.]]],.]
[1,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[[.,.],.]],.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0,0]=>[[.,[[[.,.],[[.,[.,.]],[.,.]]],.]],[[[.,[.,.]],.],.]]
[1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[[.,[[.,[.,.]],[[.,.],.]]],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,0]=>[[[[.,[.,.]],[[.,.],.]],[.,[[[.,[.,.]],.],[.,.]]]],.]
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[[[[[.,[[[.,.],.],.]],[.,.]],.],[[[.,[.,.]],.],.]],.]
[1,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0,0]=>[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,0]=>[[[[[.,[.,.]],[[.,[.,.]],.]],.],[[.,[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0]=>[[[.,[[.,[.,.]],[[.,[.,.]],.]]],[[[.,.],.],[.,.]]],.]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[[[.,[[[.,.],[.,.]],[.,[.,.]]]],[[[.,[.,.]],.],.]],.]
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[[.,[[[.,.],[[.,.],.]],.]],[[[.,[[[.,.],.],.]],.],.]]
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,0]=>[[[[[.,[.,.]],[.,.]],.],[[[.,[[[.,.],.],.]],.],.]],.]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,0]=>[[[.,[[[.,.],.],[.,.]]],[[[.,[[[.,.],.],.]],.],.]],.]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[[[.,[[[.,.],[.,.]],[[[.,[.,.]],.],.]]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[[.,[[[.,.],[.,.]],[.,[[[.,.],.],.]]]],[.,[.,.]]],.]
[1,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[.,.]],.],[.,[[[.,[.,.]],[[.,.],.]],.]]]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0,0]=>[[.,[[[.,.],[[.,[.,.]],[.,.]]],.]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0,0]=>[[.,[[.,[.,.]],[.,.]]],[.,[[[[.,.],.],[[.,.],.]],.]]]
[1,1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[.,[[[[.,[.,.]],.],[.,.]],.]]],.]
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,0]=>[[[[[.,[[[.,.],.],.]],[.,.]],.],[.,[[[.,.],.],.]]],.]
[1,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0,0]=>[[.,[[[.,[.,.]],[.,[.,.]]],.]],[[[.,.],[[.,.],.]],.]]
[1,1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,0]=>[[[[[.,[.,.]],[.,[.,.]]],.],[[[.,[.,.]],[.,.]],.]],.]
[1,1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,0]=>[[[.,[[.,[.,.]],[.,[.,.]]]],[[[[.,.],.],[.,.]],.]],.]
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,0]=>[[[.,[[[.,.],[.,.]],[.,[.,.]]]],[.,[[[.,.],.],.]]],.]
[1,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0,0]=>[[.,[[[.,[.,.]],[[.,.],.]],.]],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,0]=>[[[[[.,[.,.]],[[.,.],.]],.],[.,[[.,[.,.]],[.,.]]]],.]
[1,1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,0]=>[[[.,[[.,[.,.]],[[.,.],.]]],[.,[[[.,.],.],[.,.]]]],.]
[1,1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0]=>[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,.],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[[[.,[[[.,.],[.,.]],.]],[[[.,[[[.,.],.],.]],.],.]],.]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,[[[.,.],[[.,.],.]],.]]]
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[[[[[.,[.,.]],[.,.]],.],[.,[[[.,[.,.]],[.,.]],.]]],.]
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[[[.,[[.,[.,.]],[.,.]]],[.,[[[[.,.],.],[.,.]],.]]],.]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[[[.,[[[.,[.,.]],[.,[.,.]]],.]],[[[.,.],[.,.]],.]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[[[.,[[[.,[.,.]],[[.,.],.]],.]],[.,[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],[.,[[[.,.],[.,.]],.]]],.]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]],[[[.,[.,.]],.],.]]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[[.,[.,.]],.],.],[[.,[.,.]],.]],[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0,1,0]=>[[[[[.,[.,.]],.],[[.,[.,.]],.]],[[[.,.],.],[.,[.,.]]]],[[.,[.,.]],[.,.]]]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,0,0,0,0,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,1,0]=>[[[[[.,.],[[.,[.,.]],.]],[[.,.],[[.,[.,.]],.]]],[[[.,.],[.,[.,.]]],[[[.,.],.],.]]],[[[.,.],[[.,.],.]],[[.,.],[.,[.,.]]]]]
          

click to show experimental identities

Description

Francon's map from Dyck paths to binary trees.
This bijection sends the logarithmic height of the Dyck path, St000920The logarithmic height of a Dyck path., to the pruning number of the binary tree, St000396The register function (or Horton-Strahler number) of a binary tree.. The implementation is a literal translation of Knuth's [2].

References

[1] Françon, J. Sur le nombre de registres nécessaires à l'évaluation d'une expression arithmétique MathSciNet:0775838
[2] http://www-cs-faculty.stanford.edu/~knuth/programs/francon.w

Properties

bijective, graded

Sage code

def mapping(D):
    def LR_to_binary_tree(links, root=0):
        if links[root][0] != 0:
            left = LR_to_binary_tree(links, root=links[root][0])
        else:
            left = None

        if links[root][1] != 0:
            right = LR_to_binary_tree(links, root=links[root][1])
        else:
            right = None
        return BinaryTree([left, right])


    n = D.semilength()
    d = list(D) + [0]
    l = [0]*(n)
    r = [0]*(n)
    h = [0]*(2*n+3)
    q = [0]*(n+1)
    qm = [0]*(n+1)
    h[1] = m = 1; k = 2; p = 0
    while True:
        while h[k] != 0:
            k = k + 2
        kk = h[k//2]
        p += 1
        if d[p] == 1:
            l[kk-1] = m; m += 1; h[k] = m;
        else:
            l[kk-1] = 0
        p += 1
        if d[p] == 1:
            r[kk-1] = m; m += 1; h[k+1] = m;
        else:
            r[kk-1] = 0
        if h[k] != 0:
            if h[k+1] != 0:
                continue
            else:
                kk = k
        elif h[k+1] != 0:
            kk = k+1
        else:
            h[k//2] = 0; kk = (k//2) ^^ 1; k = kk & -2
            if k == 0:
                return LR_to_binary_tree(list(zip(l, r)))
        j = 0; jj = 1; q[0] = kk; qm[0] = 1
        while j < jj:
            kk = q[j]
            h[((kk//2)&(-qm[j]))+(kk&(qm[j]-1))] = h[kk]
            if h[2*kk] != 0:
                q[jj] = 2*kk
                q[jj+1] = 2*kk+1
                qm[jj] = qm[jj+1] = qm[j]*2
                jj = jj + 2
            else:
                h[kk] = 0
            j += 1

Created

Jan 31, 2020 at 19:19 by FindStatCrew

Updated

Jan 31, 2020 at 19:19 by Martin Rubey