Identifier
-
Mp00029:
Dyck paths
—to binary tree: left tree, up step, right tree, down step⟶
Binary trees
St000201: Binary trees ⟶ ℤ (values match St000196The number of occurrences of the contiguous pattern [[.,.],[.,.)
Values
=>
Cc0005;cc-rep-0
Cc0010;cc-rep
[1,0]=>[.,.]=>1
[1,0,1,0]=>[[.,.],.]=>1
[1,1,0,0]=>[.,[.,.]]=>1
[1,0,1,0,1,0]=>[[[.,.],.],.]=>1
[1,0,1,1,0,0]=>[[.,.],[.,.]]=>2
[1,1,0,0,1,0]=>[[.,[.,.]],.]=>1
[1,1,0,1,0,0]=>[.,[[.,.],.]]=>1
[1,1,1,0,0,0]=>[.,[.,[.,.]]]=>1
[1,0,1,0,1,0,1,0]=>[[[[.,.],.],.],.]=>1
[1,0,1,0,1,1,0,0]=>[[[.,.],.],[.,.]]=>2
[1,0,1,1,0,0,1,0]=>[[[.,.],[.,.]],.]=>2
[1,0,1,1,0,1,0,0]=>[[.,.],[[.,.],.]]=>2
[1,0,1,1,1,0,0,0]=>[[.,.],[.,[.,.]]]=>2
[1,1,0,0,1,0,1,0]=>[[[.,[.,.]],.],.]=>1
[1,1,0,0,1,1,0,0]=>[[.,[.,.]],[.,.]]=>2
[1,1,0,1,0,0,1,0]=>[[.,[[.,.],.]],.]=>1
[1,1,0,1,0,1,0,0]=>[.,[[[.,.],.],.]]=>1
[1,1,0,1,1,0,0,0]=>[.,[[.,.],[.,.]]]=>2
[1,1,1,0,0,0,1,0]=>[[.,[.,[.,.]]],.]=>1
[1,1,1,0,0,1,0,0]=>[.,[[.,[.,.]],.]]=>1
[1,1,1,0,1,0,0,0]=>[.,[.,[[.,.],.]]]=>1
[1,1,1,1,0,0,0,0]=>[.,[.,[.,[.,.]]]]=>1
[1,0,1,0,1,0,1,0,1,0]=>[[[[[.,.],.],.],.],.]=>1
[1,0,1,0,1,0,1,1,0,0]=>[[[[.,.],.],.],[.,.]]=>2
[1,0,1,0,1,1,0,0,1,0]=>[[[[.,.],.],[.,.]],.]=>2
[1,0,1,0,1,1,0,1,0,0]=>[[[.,.],.],[[.,.],.]]=>2
[1,0,1,0,1,1,1,0,0,0]=>[[[.,.],.],[.,[.,.]]]=>2
[1,0,1,1,0,0,1,0,1,0]=>[[[[.,.],[.,.]],.],.]=>2
[1,0,1,1,0,0,1,1,0,0]=>[[[.,.],[.,.]],[.,.]]=>3
[1,0,1,1,0,1,0,0,1,0]=>[[[.,.],[[.,.],.]],.]=>2
[1,0,1,1,0,1,0,1,0,0]=>[[.,.],[[[.,.],.],.]]=>2
[1,0,1,1,0,1,1,0,0,0]=>[[.,.],[[.,.],[.,.]]]=>3
[1,0,1,1,1,0,0,0,1,0]=>[[[.,.],[.,[.,.]]],.]=>2
[1,0,1,1,1,0,0,1,0,0]=>[[.,.],[[.,[.,.]],.]]=>2
[1,0,1,1,1,0,1,0,0,0]=>[[.,.],[.,[[.,.],.]]]=>2
[1,0,1,1,1,1,0,0,0,0]=>[[.,.],[.,[.,[.,.]]]]=>2
[1,1,0,0,1,0,1,0,1,0]=>[[[[.,[.,.]],.],.],.]=>1
[1,1,0,0,1,0,1,1,0,0]=>[[[.,[.,.]],.],[.,.]]=>2
[1,1,0,0,1,1,0,0,1,0]=>[[[.,[.,.]],[.,.]],.]=>2
[1,1,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[.,.],.]]=>2
[1,1,0,0,1,1,1,0,0,0]=>[[.,[.,.]],[.,[.,.]]]=>2
[1,1,0,1,0,0,1,0,1,0]=>[[[.,[[.,.],.]],.],.]=>1
[1,1,0,1,0,0,1,1,0,0]=>[[.,[[.,.],.]],[.,.]]=>2
[1,1,0,1,0,1,0,0,1,0]=>[[.,[[[.,.],.],.]],.]=>1
[1,1,0,1,0,1,0,1,0,0]=>[.,[[[[.,.],.],.],.]]=>1
[1,1,0,1,0,1,1,0,0,0]=>[.,[[[.,.],.],[.,.]]]=>2
[1,1,0,1,1,0,0,0,1,0]=>[[.,[[.,.],[.,.]]],.]=>2
[1,1,0,1,1,0,0,1,0,0]=>[.,[[[.,.],[.,.]],.]]=>2
[1,1,0,1,1,0,1,0,0,0]=>[.,[[.,.],[[.,.],.]]]=>2
[1,1,0,1,1,1,0,0,0,0]=>[.,[[.,.],[.,[.,.]]]]=>2
[1,1,1,0,0,0,1,0,1,0]=>[[[.,[.,[.,.]]],.],.]=>1
[1,1,1,0,0,0,1,1,0,0]=>[[.,[.,[.,.]]],[.,.]]=>2
[1,1,1,0,0,1,0,0,1,0]=>[[.,[[.,[.,.]],.]],.]=>1
[1,1,1,0,0,1,0,1,0,0]=>[.,[[[.,[.,.]],.],.]]=>1
[1,1,1,0,0,1,1,0,0,0]=>[.,[[.,[.,.]],[.,.]]]=>2
[1,1,1,0,1,0,0,0,1,0]=>[[.,[.,[[.,.],.]]],.]=>1
[1,1,1,0,1,0,0,1,0,0]=>[.,[[.,[[.,.],.]],.]]=>1
[1,1,1,0,1,0,1,0,0,0]=>[.,[.,[[[.,.],.],.]]]=>1
[1,1,1,0,1,1,0,0,0,0]=>[.,[.,[[.,.],[.,.]]]]=>2
[1,1,1,1,0,0,0,0,1,0]=>[[.,[.,[.,[.,.]]]],.]=>1
[1,1,1,1,0,0,0,1,0,0]=>[.,[[.,[.,[.,.]]],.]]=>1
[1,1,1,1,0,0,1,0,0,0]=>[.,[.,[[.,[.,.]],.]]]=>1
[1,1,1,1,0,1,0,0,0,0]=>[.,[.,[.,[[.,.],.]]]]=>1
[1,1,1,1,1,0,0,0,0,0]=>[.,[.,[.,[.,[.,.]]]]]=>1
[1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],.],.],.],.],.]=>1
[1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,.],.],.],.],[.,.]]=>2
[1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],.],.],[.,.]],.]=>2
[1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[.,.],.],.],[[.,.],.]]=>2
[1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,.],.],.],[.,[.,.]]]=>2
[1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[.,.],.],[.,.]],.],.]=>2
[1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[.,.],.],[.,.]],[.,.]]=>3
[1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[.,.],.],[[.,.],.]],.]=>2
[1,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,.],.],[[[.,.],.],.]]=>2
[1,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,.],.],[[.,.],[.,.]]]=>3
[1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,.],.],[.,[.,.]]],.]=>2
[1,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,.],.],[[.,[.,.]],.]]=>2
[1,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,.],.],[.,[[.,.],.]]]=>2
[1,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,.],.],[.,[.,[.,.]]]]=>2
[1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[.,.],[.,.]],.],.],.]=>2
[1,0,1,1,0,0,1,0,1,1,0,0]=>[[[[.,.],[.,.]],.],[.,.]]=>3
[1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,.]],[.,.]],.]=>3
[1,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,.],[.,.]],[[.,.],.]]=>3
[1,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,.],[.,.]],[.,[.,.]]]=>3
[1,0,1,1,0,1,0,0,1,0,1,0]=>[[[[.,.],[[.,.],.]],.],.]=>2
[1,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,.],.]],[.,.]]=>3
[1,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[.,.],.],.]],.]=>2
[1,0,1,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[.,.],.],.],.]]=>2
[1,0,1,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,.],.],[.,.]]]=>3
[1,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,.],[.,.]]],.]=>3
[1,0,1,1,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,.],[.,.]],.]]=>3
[1,0,1,1,0,1,1,0,1,0,0,0]=>[[.,.],[[.,.],[[.,.],.]]]=>3
[1,0,1,1,0,1,1,1,0,0,0,0]=>[[.,.],[[.,.],[.,[.,.]]]]=>3
[1,0,1,1,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,.]]],.],.]=>2
[1,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,.]]],[.,.]]=>3
[1,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,.]],.]],.]=>2
[1,0,1,1,1,0,0,1,0,1,0,0]=>[[.,.],[[[.,[.,.]],.],.]]=>2
[1,0,1,1,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[.,.]],[.,.]]]=>3
[1,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,.],[.,[[.,.],.]]],.]=>2
[1,0,1,1,1,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,.],.]],.]]=>2
[1,0,1,1,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[.,.],.],.]]]=>2
[1,0,1,1,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[.,.],[.,.]]]]=>3
[1,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,.]]]],.]=>2
[1,0,1,1,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[.,[.,.]]],.]]=>2
[1,0,1,1,1,1,0,0,1,0,0,0]=>[[.,.],[.,[[.,[.,.]],.]]]=>2
[1,0,1,1,1,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[.,.],.]]]]=>2
[1,0,1,1,1,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,.]]]]]=>2
[1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,.]],.],.],.],.]=>1
[1,1,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[.,.]],.],.],[.,.]]=>2
[1,1,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,.]],.],[.,.]],.]=>2
[1,1,0,0,1,0,1,1,0,1,0,0]=>[[[.,[.,.]],.],[[.,.],.]]=>2
[1,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,.]],.],[.,[.,.]]]=>2
[1,1,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,.]],.],.]=>2
[1,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,.]],[.,.]],[.,.]]=>3
[1,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,.],.]],.]=>2
[1,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,.],.],.]]=>2
[1,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,.]],[[.,.],[.,.]]]=>3
[1,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,.]]],.]=>2
[1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,.]],.]]=>2
[1,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[.,.],.]]]=>2
[1,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,.]]]]=>2
[1,1,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[.,.],.]],.],.],.]=>1
[1,1,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[.,.],.]],.],[.,.]]=>2
[1,1,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],.]],[.,.]],.]=>2
[1,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,.],.]],[[.,.],.]]=>2
[1,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[[.,.],.]],[.,[.,.]]]=>2
[1,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[.,.],.],.]],.],.]=>1
[1,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],.],.]],[.,.]]=>2
[1,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[.,.],.],.],.]],.]=>1
[1,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,.],.],.],.],.]]=>1
[1,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[.,.],.],.],[.,.]]]=>2
[1,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[.,.],.],[.,.]]],.]=>2
[1,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[.,.],.],[.,.]],.]]=>2
[1,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,.],.],[[.,.],.]]]=>2
[1,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[.,.],.],[.,[.,.]]]]=>2
[1,1,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[.,.],[.,.]]],.],.]=>2
[1,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[.,.]]],[.,.]]=>3
[1,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[.,.],[.,.]],.]],.]=>2
[1,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[.,.],[.,.]],.],.]]=>2
[1,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[.,.]],[.,.]]]=>3
[1,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,.],[[.,.],.]]],.]=>2
[1,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,.],.]],.]]=>2
[1,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[.,.],.],.]]]=>2
[1,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[.,.],[.,.]]]]=>3
[1,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[[.,.],[.,[.,.]]]],.]=>2
[1,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[[.,.],[.,[.,.]]],.]]=>2
[1,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[.,.]],.]]]=>2
[1,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[.,.],[.,[[.,.],.]]]]=>2
[1,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,.]]]]]=>2
[1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,.]]],.],.],.]=>1
[1,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[.,.]]],.],[.,.]]=>2
[1,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,.]]],[.,.]],.]=>2
[1,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,[.,.]]],[[.,.],.]]=>2
[1,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,.]]],[.,[.,.]]]=>2
[1,1,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[.,.]],.]],.],.]=>1
[1,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,.]],.]],[.,.]]=>2
[1,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[.,.]],.],.]],.]=>1
[1,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[.,.]],.],.],.]]=>1
[1,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,.]],.],[.,.]]]=>2
[1,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[.,.]]],.]=>2
[1,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[.,.]],.]]=>2
[1,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[.,.],.]]]=>2
[1,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[.,[.,.]],[.,[.,.]]]]=>2
[1,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[.,.],.]]],.],.]=>1
[1,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,.],.]]],[.,.]]=>2
[1,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,.],.]],.]],.]=>1
[1,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],.]],.],.]]=>1
[1,1,1,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],.]],[.,.]]]=>2
[1,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[.,.],.],.]]],.]=>1
[1,1,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[.,.],.],.]],.]]=>1
[1,1,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[.,.],.],.],.]]]=>1
[1,1,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[.,.],.],[.,.]]]]=>2
[1,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[.,.],[.,.]]]],.]=>2
[1,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[.,.],[.,.]]],.]]=>2
[1,1,1,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[.,.],[.,.]],.]]]=>2
[1,1,1,0,1,1,0,1,0,0,0,0]=>[.,[.,[[.,.],[[.,.],.]]]]=>2
[1,1,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,.]]]]]=>2
[1,1,1,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,.]]]],.],.]=>1
[1,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,.]]]],[.,.]]=>2
[1,1,1,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,.]]],.]],.]=>1
[1,1,1,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[.,.]]],.],.]]=>1
[1,1,1,1,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[.,.]]],[.,.]]]=>2
[1,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,.]],.]]],.]=>1
[1,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[.,.]],.]],.]]=>1
[1,1,1,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,.]],.],.]]]=>1
[1,1,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[.,.]],[.,.]]]]=>2
[1,1,1,1,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[.,.],.]]]],.]=>1
[1,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[.,.],.]]],.]]=>1
[1,1,1,1,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[.,.],.]],.]]]=>1
[1,1,1,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[.,.],.],.]]]]=>1
[1,1,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,.]]]]]=>2
[1,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,.]]]]],.]=>1
[1,1,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,.]]]],.]]=>1
[1,1,1,1,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,.]]],.]]]=>1
[1,1,1,1,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[.,.]],.]]]]=>1
[1,1,1,1,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],.]]]]]=>1
[1,1,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],.],.],.],.],.],.]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[.,.],.],.],.],.],[.,.]]=>2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[.,.],.],.],.],[.,.]],.]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[.,.],.],.],.],[[.,.],.]]=>2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[.,.],.],.],[.,.]],.],.]=>2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>3
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[.,.],.],.],[[.,.],.]],.]=>2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[.,.],.],.],[[[.,.],.],.]]=>2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[.,.],.],[.,.]],.],.],.]=>2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[[[[.,.],.],[[.,.],.]],.],.]=>2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>3
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[[[.,.],.],[[[.,.],.],.]],.]=>2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[[[.,.],.],.],.]]=>2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>3
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>3
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>3
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[.,.]],.],.],.],.]=>2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>3
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>4
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>4
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>3
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[[[[.,.],[[.,.],.]],.],.],.]=>2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[[[.,.],[[[.,.],.],.]],.],.]=>2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[.,.],.],.],.]],.]=>2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[.,.],.],.],.],.]]=>2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>3
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>4
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>4
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>3
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>4
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>3
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>3
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[[[.,.],[[.,[.,.]],.]],.],.]=>2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>3
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,[[.,.],.]]],.],.]=>2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>3
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>3
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>3
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>3
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>3
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,.]],.],.],.],.],.]=>1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>3
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>3
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>3
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>3
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>3
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[[.,.],.]],.],.],.],.]=>1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[.,.],.]],[.,.]],.],.]=>2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>3
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>3
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[[.,.],.],.]],.],.],.]=>1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[[.,.],.],.],.]],.],.]=>1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[.,.],.],.],.],.]],.]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],.],.],.],.],.]]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[[.,.],.],.],[.,.]]],.]=>2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[[.,.],.],[.,.]]],.],.]=>2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>3
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[[.,.],.],[.,.]],.]],.]=>2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[[.,.],.],[.,.]],.],.]]=>2
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>3
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[[.,.],[.,.]]],.],.],.]=>2
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>3
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[[.,.],[.,.]],.]],.],.]=>2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>3
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[[.,.],[.,.]],.],.]],.]=>2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[[.,.],[.,.]],.],.],.]]=>2
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>3
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>3
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>3
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,[[.,.],[[.,.],.]]],.],.]=>2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>3
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[[[.,.],[[.,.],.]],.]],.]=>2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[[[.,.],[[.,.],.]],.],.]]=>2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,.],[[[.,.],.],.]]],.]=>2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[.,[[[.,.],[[[.,.],.],.]],.]]=>2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>3
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>3
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>3
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>3
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,.],[.,[.,.]]]],.],.]=>2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>3
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],[.,[.,.]]],.]],.]=>2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[.,[[[[.,.],[.,[.,.]]],.],.]]=>2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>3
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[[.,.],[[.,[.,.]],.]]],.]=>2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[.,.]],.]],.]]=>2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[.,[[.,.],[[[.,[.,.]],.],.]]]=>2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[.,[[.,.],[.,[[.,.],.]]]],.]=>2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,.],[.,[[.,.],.]]],.]]=>2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,.],.]],.]]]=>2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]=>2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]=>2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]=>2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]=>2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>3
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[.,[.,.]],.],.],.]],.]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[.,.]],.],.],.],.]]=>1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[.,[.,.]],.],.],[.,.]]]=>2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[.,[.,.]],.],[.,.]]],.]=>2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],.],[.,.]],.]]=>2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[.,[.,.]],[.,.]]],.],.]=>2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>3
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[.,[.,.]],[.,.]],.]],.]=>2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[.,[.,.]],[.,.]],.],.]]=>2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>3
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,.],.]],.]]=>2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>3
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]=>2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[[.,.],.]]],.],.],.]=>1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[[.,.],.]],.],.]],.]=>1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[[.,.],.]],.],.],.]]=>1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[.,.],.]],.],[.,.]]]=>2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[.,.]],.]]=>2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[[.,.],.],.]]],.],.]=>1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,.],.],.]],.]],.]=>1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[[.,.],.],.]],.],.]]=>1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[[.,.],.],.]],[.,.]]]=>2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[[.,.],.],.],.]]],.]=>1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,.],.],.],.]],.]]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[.,.],.],.],.],.]]]=>1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[[.,.],.],[.,.]]]],.]=>2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[[.,.],.],[.,.]]],.]]=>2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[[.,.],.],[.,.]],.]]]=>2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[[.,.],[.,.]]]],.],.]=>2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>3
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,.],[.,.]]],.]],.]=>2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],.]]=>2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>3
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[[.,.],[.,.]],.]]],.]=>2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,.],[.,.]],.]],.]]=>2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[[.,.],[.,.]],.],.]]]=>2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[.,[[.,.],[[.,.],.]]]],.]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,.],.]]],.]]=>2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[.,[.,[[[.,.],[[.,.],.]],.]]]=>2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]=>2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]=>2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]=>2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]=>2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[.,[.,.]]],.],.]],.]=>1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[.,[.,.]]],.],.],.]]=>1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]=>2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]=>2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[.,[.,.]],.]]],.],.]=>1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[.,.]],.]],.],.]]=>1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[.,[.,.]],.],.]]],.]=>1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],.],.]],.]]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[.,[.,.]],.],.],.]]]=>1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]=>2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]=>2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]=>2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]=>2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[[.,.],.]]]],.],.]=>1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[[.,.],.]]],.]],.]=>1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[[.,.],.]]],.],.]]=>1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]=>2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[[.,.],.]],.]]],.]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,.],.]],.]],.]]=>1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[[.,.],.]],.],.]]]=>1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]=>2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[[.,.],.],.]]]],.]=>1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[[.,.],.],.]]],.]]=>1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[[.,.],.],.]],.]]]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[.,.],.],.],.]]]]=>1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]=>2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]=>2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]=>2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]=>2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[.,[.,.]]]],.],.]]=>1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]=>1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[.,[.,.]]],.]],.]]=>1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]=>1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]=>1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[.,[.,.]],.]]],.]]=>1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[.,[.,.]],.]],.]]]=>1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]=>1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]=>1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]=>1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]=>1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>2
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>3
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>2
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>3
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]=>2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>2
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>3
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>3
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>3
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>3
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>3
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>4
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>3
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>3
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>3
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]=>2
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>4
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>3
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>3
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>3
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>3
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>3
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>3
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>3
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>4
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>3
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>4
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>4
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>4
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>4
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>4
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>3
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>4
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>3
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>2
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>3
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>4
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>3
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>4
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>4
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>3
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>4
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>4
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>3
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>3
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>3
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>4
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>3
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>3
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>3
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>3
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>3
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>3
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>4
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>3
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>3
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>3
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>3
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>2
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>3
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>2
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>3
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>2
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>2
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>3
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>2
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>3
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>3
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>3
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>3
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>4
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>3
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>2
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>3
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>4
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>4
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>3
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>3
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>4
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>3
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>3
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>3
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>3
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>2
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>3
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>3
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>2
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>3
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>2
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>2
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>2
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>3
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>3
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>3
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>3
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>2
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>2
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]=>1
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>2
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>3
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>4
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>3
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>2
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>4
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>3
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>4
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>3
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>3
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>2
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>2
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>2
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>3
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>3
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>3
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>2
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>3
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>3
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>3
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>1
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>3
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>2
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>2
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>2
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>1
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>3
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>2
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>2
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>2
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>1
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>2
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>1
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>2
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>2
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]=>1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]=>2
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>2
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>3
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>2
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]=>2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>1
[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]]=>4
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>5
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]]=>5
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>5
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]=>4
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]=>4
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]=>4
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]=>3
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]=>4
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]=>3
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]=>3
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]=>3
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]=>2
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]=>4
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]=>3
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]=>3
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]=>2
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]=>4
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]=>2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]=>4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]=>3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]=>3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]=>3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]=>2
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]=>1
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]=>6
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]]=>5
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]]=>5
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]]=>5
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]]=>4
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]]=>5
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]]=>4
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]]=>5
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]]=>4
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]]=>5
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]]=>4
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]]=>4
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]]=>4
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]]=>3
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]]=>5
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]]=>4
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]]=>4
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]]=>4
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]]=>3
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.]]=>4
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.]]=>3
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]]=>4
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]]=>3
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]]=>4
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]]=>3
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]]=>3
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]]=>3
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]]=>2
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>5
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]=>4
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]=>4
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]=>4
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]=>3
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]=>4
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]=>3
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]=>3
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]=>3
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]=>2
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],[[.,.],.]]]]=>5
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],[[.,.],.]]]=>4
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],[[.,.],.]]],.]]=>4
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,[[.,[[.,.],.]],.]],.]]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],[[.,.],.]]]]=>4
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],[[.,.],.]]]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],[[.,.],.]]],.]]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,[[.,[[.,.],.]],.]],.]]=>2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],[[.,.],.]]]=>5
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,[[.,.],.]],.]]=>4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],[[.,.],.]]]=>4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],.]]=>3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],[[.,.],.]]]=>4
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,[[.,.],.]],.]]=>3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],[[.,.],.]]]=>4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,[[.,.],.]],.]]=>3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],[[.,.],.]]]=>3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,[[.,.],.]],.]]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],[[.,.],.]]=>5
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],[[.,.],.]]=>4
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],[[.,.],.]]=>4
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],[[.,.],.]]=>4
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],[[.,.],.]]=>3
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],[[.,.],.]]=>4
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],[[.,.],.]]=>3
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],[[.,.],.]]=>4
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],[[.,.],.]]=>3
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],[[.,.],.]]=>4
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],[[.,.],.]]=>3
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],[[.,.],.]]=>3
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],[[.,.],.]]=>3
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[[.,.],.]]=>2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]=>4
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]=>4
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]=>4
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]=>4
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.]=>4
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>4
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]]=>4
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>4
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]]=>3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>4
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]]=>3
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]]=>3
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]]=>3
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>4
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>3
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>3
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>4
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]]=>3
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]=>2
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]]=>2
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]=>3
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]]=>3
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]=>3
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]=>2
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]=>2
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]=>2
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]=>3
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]]=>3
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>1
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>2
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]]=>2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>3
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>3
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>3
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>3
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>3
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]]=>2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>3
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>6
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],[.,.]]=>5
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],[.,.]]=>4
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]=>5
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],[.,.]]=>5
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]]=>4
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],[.,.]]=>4
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],[.,.]]=>4
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],[.,.]]=>3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>5
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>4
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],[.,.]]=>4
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]=>5
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],[.,.]]=>5
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]]=>4
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],[.,.]]=>3
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],[.,.]]=>3
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]]=>4
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],[.,.]]=>4
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],[.,.]]=>4
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],[.,.]]=>3
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],[.,.]]=>3
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],[.,.]]=>3
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]]=>4
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],[.,.]]=>4
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],[.,.]]=>2
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>3
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>5
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>4
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],[.,.]]=>3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>4
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>4
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>4
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>4
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],[.,.]]=>4
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],[.,.]]=>3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>5
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>4
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],[.,.]]=>4
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]=>5
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]]=>5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]]=>4
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[[.,[[.,[.,.]],.]],.]]=>3
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[[.,[[.,[.,.]],.]],.]]=>2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]=>3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[[.,[[.,[.,.]],.]],.]]=>3
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]]=>3
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],.]]=>3
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],.]]=>3
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],.]]=>2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]=>4
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]=>3
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],.]]=>3
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]]=>4
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],.]]=>4
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]=>4
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]=>4
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],.]]=>2
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]=>3
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]=>3
[1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]=>3
[1,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]=>3
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],.]]=>2
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]=>3
[1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]=>3
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],.]]=>4
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],.]]=>3
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],.]]=>3
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],.]]=>3
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],.]]=>2
[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
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],.]]=>3
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],.]]=>3
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.]]=>2
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],.]]=>3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]=>4
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]=>3
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],.]]=>3
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]]=>4
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],.]]=>4
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>2
[1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>2
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],.]]=>2
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],.]]=>2
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>3
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>2
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],.]]=>2
[1,1,0,0,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]]=>3
[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],.]]=>3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>5
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>4
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[[.,[.,.]],.]]=>3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>4
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>4
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>3
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>3
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[[.,[.,.]],.]]=>3
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[[.,[.,.]],.]]=>2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>4
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>3
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]]=>3
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>4
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>4
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>4
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>3
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]]=>3
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>4
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>4
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]]=>4
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]]=>3
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],.]]=>3
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],.]]=>3
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>4
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>4
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],.]]=>2
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]]=>3
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],.]]=>3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]]=>5
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[[[.,[.,.]],[.,.]],.]]=>4
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[[[.,[.,.]],[.,.]],.]]=>3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>4
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>4
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>4
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>4
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]]=>4
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],.]]=>3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>5
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>4
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]]=>4
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]=>5
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]]=>5
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]=>5
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]]=>4
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]=>5
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]]=>4
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]]=>3
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],[[.,[[.,.],[.,.]]],.]]]=>4
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[[.,.],[.,.]]]]=>4
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]]=>2
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]]=>3
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Description
The number of leaf nodes in a binary tree.
Equivalently, the number of cherries [1] in the complete binary tree.
The number of binary trees of size $n$, at least $1$, with exactly one leaf node for is $2^{n-1}$, see [2].
The number of binary tree of size $n$, at least $3$, with exactly two leaf nodes is $n(n+1)2^{n-2}$, see [3].
Equivalently, the number of cherries [1] in the complete binary tree.
The number of binary trees of size $n$, at least $1$, with exactly one leaf node for is $2^{n-1}$, see [2].
The number of binary tree of size $n$, at least $3$, with exactly two leaf nodes is $n(n+1)2^{n-2}$, see [3].
Map
to binary tree: left tree, up step, right tree, down step
Description
Return the binary tree corresponding to the Dyck path under the transformation left tree - up step - right tree - down step.
A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ for Dyck paths $L,R$ of respective semilengths $n_1,n_2$ with $n_1+n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.
A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ for Dyck paths $L,R$ of respective semilengths $n_1,n_2$ with $n_1+n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.
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