Identifier
-
Mp00029:
Dyck paths
—to binary tree: left tree, up step, right tree, down step⟶
Binary trees
St000118: Binary trees ⟶ ℤ
Values
=>
Cc0005;cc-rep-0
Cc0010;cc-rep
[1,0]=>[.,.]=>0
[1,0,1,0]=>[[.,.],.]=>0
[1,1,0,0]=>[.,[.,.]]=>0
[1,0,1,0,1,0]=>[[[.,.],.],.]=>0
[1,0,1,1,0,0]=>[[.,.],[.,.]]=>0
[1,1,0,0,1,0]=>[[.,[.,.]],.]=>0
[1,1,0,1,0,0]=>[.,[[.,.],.]]=>0
[1,1,1,0,0,0]=>[.,[.,[.,.]]]=>1
[1,0,1,0,1,0,1,0]=>[[[[.,.],.],.],.]=>0
[1,0,1,0,1,1,0,0]=>[[[.,.],.],[.,.]]=>0
[1,0,1,1,0,0,1,0]=>[[[.,.],[.,.]],.]=>0
[1,0,1,1,0,1,0,0]=>[[.,.],[[.,.],.]]=>0
[1,0,1,1,1,0,0,0]=>[[.,.],[.,[.,.]]]=>1
[1,1,0,0,1,0,1,0]=>[[[.,[.,.]],.],.]=>0
[1,1,0,0,1,1,0,0]=>[[.,[.,.]],[.,.]]=>0
[1,1,0,1,0,0,1,0]=>[[.,[[.,.],.]],.]=>0
[1,1,0,1,0,1,0,0]=>[.,[[[.,.],.],.]]=>0
[1,1,0,1,1,0,0,0]=>[.,[[.,.],[.,.]]]=>1
[1,1,1,0,0,0,1,0]=>[[.,[.,[.,.]]],.]=>1
[1,1,1,0,0,1,0,0]=>[.,[[.,[.,.]],.]]=>0
[1,1,1,0,1,0,0,0]=>[.,[.,[[.,.],.]]]=>1
[1,1,1,1,0,0,0,0]=>[.,[.,[.,[.,.]]]]=>2
[1,0,1,0,1,0,1,0,1,0]=>[[[[[.,.],.],.],.],.]=>0
[1,0,1,0,1,0,1,1,0,0]=>[[[[.,.],.],.],[.,.]]=>0
[1,0,1,0,1,1,0,0,1,0]=>[[[[.,.],.],[.,.]],.]=>0
[1,0,1,0,1,1,0,1,0,0]=>[[[.,.],.],[[.,.],.]]=>0
[1,0,1,0,1,1,1,0,0,0]=>[[[.,.],.],[.,[.,.]]]=>1
[1,0,1,1,0,0,1,0,1,0]=>[[[[.,.],[.,.]],.],.]=>0
[1,0,1,1,0,0,1,1,0,0]=>[[[.,.],[.,.]],[.,.]]=>0
[1,0,1,1,0,1,0,0,1,0]=>[[[.,.],[[.,.],.]],.]=>0
[1,0,1,1,0,1,0,1,0,0]=>[[.,.],[[[.,.],.],.]]=>0
[1,0,1,1,0,1,1,0,0,0]=>[[.,.],[[.,.],[.,.]]]=>1
[1,0,1,1,1,0,0,0,1,0]=>[[[.,.],[.,[.,.]]],.]=>1
[1,0,1,1,1,0,0,1,0,0]=>[[.,.],[[.,[.,.]],.]]=>0
[1,0,1,1,1,0,1,0,0,0]=>[[.,.],[.,[[.,.],.]]]=>1
[1,0,1,1,1,1,0,0,0,0]=>[[.,.],[.,[.,[.,.]]]]=>2
[1,1,0,0,1,0,1,0,1,0]=>[[[[.,[.,.]],.],.],.]=>0
[1,1,0,0,1,0,1,1,0,0]=>[[[.,[.,.]],.],[.,.]]=>0
[1,1,0,0,1,1,0,0,1,0]=>[[[.,[.,.]],[.,.]],.]=>0
[1,1,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[.,.],.]]=>0
[1,1,0,0,1,1,1,0,0,0]=>[[.,[.,.]],[.,[.,.]]]=>1
[1,1,0,1,0,0,1,0,1,0]=>[[[.,[[.,.],.]],.],.]=>0
[1,1,0,1,0,0,1,1,0,0]=>[[.,[[.,.],.]],[.,.]]=>0
[1,1,0,1,0,1,0,0,1,0]=>[[.,[[[.,.],.],.]],.]=>0
[1,1,0,1,0,1,0,1,0,0]=>[.,[[[[.,.],.],.],.]]=>0
[1,1,0,1,0,1,1,0,0,0]=>[.,[[[.,.],.],[.,.]]]=>1
[1,1,0,1,1,0,0,0,1,0]=>[[.,[[.,.],[.,.]]],.]=>1
[1,1,0,1,1,0,0,1,0,0]=>[.,[[[.,.],[.,.]],.]]=>0
[1,1,0,1,1,0,1,0,0,0]=>[.,[[.,.],[[.,.],.]]]=>1
[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]=>[[.,[.,[.,.]]],[.,.]]=>1
[1,1,1,0,0,1,0,0,1,0]=>[[.,[[.,[.,.]],.]],.]=>0
[1,1,1,0,0,1,0,1,0,0]=>[.,[[[.,[.,.]],.],.]]=>0
[1,1,1,0,0,1,1,0,0,0]=>[.,[[.,[.,.]],[.,.]]]=>1
[1,1,1,0,1,0,0,0,1,0]=>[[.,[.,[[.,.],.]]],.]=>1
[1,1,1,0,1,0,0,1,0,0]=>[.,[[.,[[.,.],.]],.]]=>0
[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]=>[[.,[.,[.,[.,.]]]],.]=>2
[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]=>[.,[.,[.,[[.,.],.]]]]=>2
[1,1,1,1,1,0,0,0,0,0]=>[.,[.,[.,[.,[.,.]]]]]=>3
[1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],.],.],.],.],.]=>0
[1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,.],.],.],.],[.,.]]=>0
[1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],.],.],[.,.]],.]=>0
[1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[.,.],.],.],[[.,.],.]]=>0
[1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,.],.],.],[.,[.,.]]]=>1
[1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[.,.],.],[.,.]],.],.]=>0
[1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[.,.],.],[.,.]],[.,.]]=>0
[1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[.,.],.],[[.,.],.]],.]=>0
[1,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,.],.],[[[.,.],.],.]]=>0
[1,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,.],.],[[.,.],[.,.]]]=>1
[1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,.],.],[.,[.,.]]],.]=>1
[1,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,.],.],[[.,[.,.]],.]]=>0
[1,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,.],.],[.,[[.,.],.]]]=>1
[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]=>[[[[[.,.],[.,.]],.],.],.]=>0
[1,0,1,1,0,0,1,0,1,1,0,0]=>[[[[.,.],[.,.]],.],[.,.]]=>0
[1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,.]],[.,.]],.]=>0
[1,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,.],[.,.]],[[.,.],.]]=>0
[1,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,.],[.,.]],[.,[.,.]]]=>1
[1,0,1,1,0,1,0,0,1,0,1,0]=>[[[[.,.],[[.,.],.]],.],.]=>0
[1,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,.],.]],[.,.]]=>0
[1,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[.,.],.],.]],.]=>0
[1,0,1,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[.,.],.],.],.]]=>0
[1,0,1,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,.],.],[.,.]]]=>1
[1,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,.],[.,.]]],.]=>1
[1,0,1,1,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,.],[.,.]],.]]=>0
[1,0,1,1,0,1,1,0,1,0,0,0]=>[[.,.],[[.,.],[[.,.],.]]]=>1
[1,0,1,1,0,1,1,1,0,0,0,0]=>[[.,.],[[.,.],[.,[.,.]]]]=>2
[1,0,1,1,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,.]]],.],.]=>1
[1,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,.]]],[.,.]]=>1
[1,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,.]],.]],.]=>0
[1,0,1,1,1,0,0,1,0,1,0,0]=>[[.,.],[[[.,[.,.]],.],.]]=>0
[1,0,1,1,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[.,.]],[.,.]]]=>1
[1,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,.],[.,[[.,.],.]]],.]=>1
[1,0,1,1,1,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,.],.]],.]]=>0
[1,0,1,1,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[.,.],.],.]]]=>1
[1,0,1,1,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[.,.],[.,.]]]]=>2
[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]=>[[.,.],[[.,[.,[.,.]]],.]]=>1
[1,0,1,1,1,1,0,0,1,0,0,0]=>[[.,.],[.,[[.,[.,.]],.]]]=>1
[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]=>[[.,.],[.,[.,[.,[.,.]]]]]=>3
[1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,.]],.],.],.],.]=>0
[1,1,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[.,.]],.],.],[.,.]]=>0
[1,1,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,.]],.],[.,.]],.]=>0
[1,1,0,0,1,0,1,1,0,1,0,0]=>[[[.,[.,.]],.],[[.,.],.]]=>0
[1,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,.]],.],[.,[.,.]]]=>1
[1,1,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,.]],.],.]=>0
[1,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,.]],[.,.]],[.,.]]=>0
[1,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,.],.]],.]=>0
[1,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,.],.],.]]=>0
[1,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,.]],[[.,.],[.,.]]]=>1
[1,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,.]]],.]=>1
[1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,.]],.]]=>0
[1,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[.,.],.]]]=>1
[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]=>[[[[.,[[.,.],.]],.],.],.]=>0
[1,1,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[.,.],.]],.],[.,.]]=>0
[1,1,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],.]],[.,.]],.]=>0
[1,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,.],.]],[[.,.],.]]=>0
[1,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[[.,.],.]],[.,[.,.]]]=>1
[1,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[.,.],.],.]],.],.]=>0
[1,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],.],.]],[.,.]]=>0
[1,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[.,.],.],.],.]],.]=>0
[1,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,.],.],.],.],.]]=>0
[1,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[.,.],.],.],[.,.]]]=>1
[1,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[.,.],.],[.,.]]],.]=>1
[1,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[.,.],.],[.,.]],.]]=>0
[1,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,.],.],[[.,.],.]]]=>1
[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]=>[[[.,[[.,.],[.,.]]],.],.]=>1
[1,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[.,.]]],[.,.]]=>1
[1,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[.,.],[.,.]],.]],.]=>0
[1,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[.,.],[.,.]],.],.]]=>0
[1,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[.,.]],[.,.]]]=>1
[1,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,.],[[.,.],.]]],.]=>1
[1,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,.],.]],.]]=>0
[1,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[.,.],.],.]]]=>1
[1,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[.,.],[.,.]]]]=>2
[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]=>[.,[[[.,.],[.,[.,.]]],.]]=>1
[1,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[.,.]],.]]]=>1
[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]=>[.,[[.,.],[.,[.,[.,.]]]]]=>3
[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]=>[[[.,[.,[.,.]]],.],[.,.]]=>1
[1,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,.]]],[.,.]],.]=>1
[1,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,[.,.]]],[[.,.],.]]=>1
[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]=>[[[.,[[.,[.,.]],.]],.],.]=>0
[1,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,.]],.]],[.,.]]=>0
[1,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[.,.]],.],.]],.]=>0
[1,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[.,.]],.],.],.]]=>0
[1,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,.]],.],[.,.]]]=>1
[1,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[.,.]]],.]=>1
[1,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[.,.]],.]]=>0
[1,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[.,.],.]]]=>1
[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]=>[[.,[.,[[.,.],.]]],[.,.]]=>1
[1,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,.],.]],.]],.]=>0
[1,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],.]],.],.]]=>0
[1,1,1,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],.]],[.,.]]]=>1
[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]=>[.,[[.,[[[.,.],.],.]],.]]=>0
[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]=>[.,[[.,[[.,.],[.,.]]],.]]=>1
[1,1,1,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[.,.],[.,.]],.]]]=>1
[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]=>[.,[.,[[.,.],[.,[.,.]]]]]=>3
[1,1,1,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,.]]]],.],.]=>2
[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]=>[.,[[.,[[.,[.,.]],.]],.]]=>0
[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]=>[[.,[.,[.,[[.,.],.]]]],.]=>2
[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]=>[.,[.,[.,[[[.,.],.],.]]]]=>2
[1,1,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,.]]]]]=>3
[1,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,.]]]]],.]=>3
[1,1,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,.]]]],.]]=>2
[1,1,1,1,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,.]]],.]]]=>2
[1,1,1,1,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[.,.]],.]]]]=>2
[1,1,1,1,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],.]]]]]=>3
[1,1,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>4
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],.],.],.],.],.],.]=>0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[.,.],.],.],.],.],[.,.]]=>0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[.,.],.],.],.],[.,.]],.]=>0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[.,.],.],.],.],[[.,.],.]]=>0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[.,.],.],.],[.,.]],.],.]=>0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[.,.],.],.],[[.,.],.]],.]=>0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[.,.],.],.],[[[.,.],.],.]]=>0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>1
[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]=>[[[[[[.,.],.],[.,.]],.],.],.]=>0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>0
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[[[[.,.],.],[[.,.],.]],.],.]=>0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[[[.,.],.],[[[.,.],.],.]],.]=>0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[[[.,.],.],.],.]]=>0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>2
[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]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>1
[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]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[.,.]],.],.],.],.]=>0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>0
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>0
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>0
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>0
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[[[[.,.],[[.,.],.]],.],.],.]=>0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>0
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>0
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[[[.,.],[[[.,.],.],.]],.],.]=>0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>0
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[.,.],.],.],.]],.]=>0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[.,.],.],.],.],.]]=>0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>2
[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]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[[[.,.],[[.,[.,.]],.]],.],.]=>0
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>0
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>0
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>0
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>0
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,[[.,.],.]]],.],.]=>1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>2
[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]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>0
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>2
[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]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>1
[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]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>3
[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]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>4
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,.]],.],.],.],.],.]=>0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>0
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>0
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>0
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>0
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>0
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>0
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>0
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>1
[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]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>0
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>0
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>0
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>0
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>0
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>0
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>0
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>0
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>0
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>0
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>2
[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]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>1
[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]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[[.,.],.]],.],.],.],.]=>0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>0
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>0
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[.,.],.]],[.,.]],.],.]=>0
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>0
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>0
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>0
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>1
[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]=>[[[[.,[[[.,.],.],.]],.],.],.]=>0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>0
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>0
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>0
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[[.,.],.],.],.]],.],.]=>0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[.,.],.],.],.],.]],.]=>0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],.],.],.],.],.]]=>0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[[.,.],.],.],[.,.]]],.]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>0
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>1
[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]=>[[[.,[[[.,.],.],[.,.]]],.],.]=>1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[[.,.],.],[.,.]],.]],.]=>0
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[[.,.],.],[.,.]],.],.]]=>0
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>2
[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]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>1
[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]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[[.,.],[.,.]]],.],.],.]=>1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[[.,.],[.,.]],.]],.],.]=>0
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>0
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[[.,.],[.,.]],.],.]],.]=>0
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[[.,.],[.,.]],.],.],.]]=>0
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>0
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,[[.,.],[[.,.],.]]],.],.]=>1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[[[.,.],[[.,.],.]],.]],.]=>0
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[[[.,.],[[.,.],.]],.],.]]=>0
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,.],[[[.,.],.],.]]],.]=>1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[.,[[[.,.],[[[.,.],.],.]],.]]=>0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>2
[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]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],[.,[.,.]]],.]],.]=>1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[.,[[[[.,.],[.,[.,.]]],.],.]]=>1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[[.,.],[[.,[.,.]],.]]],.]=>1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[.,.]],.]],.]]=>0
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[.,[[.,.],[[[.,[.,.]],.],.]]]=>1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>2
[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]=>[.,[[[.,.],[.,[[.,.],.]]],.]]=>1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,.],.]],.]]]=>1
[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]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]=>3
[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]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>3
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>4
[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]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>1
[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]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>2
[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]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>1
[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]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>0
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>0
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>0
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>0
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>0
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>0
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[.,[.,.]],.],.],.]],.]=>0
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[.,.]],.],.],.],.]]=>0
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[.,[.,.]],.],.],[.,.]]]=>1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[.,[.,.]],.],[.,.]]],.]=>1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],.],[.,.]],.]]=>0
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>1
[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]=>[[[.,[[.,[.,.]],[.,.]]],.],.]=>1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[.,[.,.]],[.,.]],.]],.]=>0
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[.,[.,.]],[.,.]],.],.]]=>0
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,.],.]],.]]=>0
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>2
[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]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]=>1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>1
[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]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>3
[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]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>1
[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]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>0
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>0
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[[.,.],.]],.],.]],.]=>0
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[[.,.],.]],.],.],.]]=>0
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[.,.],.]],.],[.,.]]]=>1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[.,.]],.]]=>0
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>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]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,.],.],.]],.]],.]=>0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[[.,.],.],.]],.],.]]=>0
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[[.,.],.],.]],[.,.]]]=>1
[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]=>[.,[[.,[[[[.,.],.],.],.]],.]]=>0
[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]=>[.,[[.,[[[.,.],.],[.,.]]],.]]=>1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[[.,.],.],[.,.]],.]]]=>1
[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]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>3
[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]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,.],[.,.]]],.]],.]=>1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],.]]=>1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[[.,.],[.,.]],.]]],.]=>1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,.],[.,.]],.]],.]]=>0
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[[.,.],[.,.]],.],.]]]=>1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>2
[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]=>[.,[[.,[[.,.],[[.,.],.]]],.]]=>1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[.,[.,[[[.,.],[[.,.],.]],.]]]=>1
[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]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]=>3
[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]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>4
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>2
[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]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>3
[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]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>1
[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]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]=>1
[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]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>3
[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]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>0
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[.,.]],.]],.],.]]=>0
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>1
[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]=>[.,[[.,[[[.,[.,.]],.],.]],.]]=>0
[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]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]=>1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]=>1
[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]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[[.,.],.]]]],.],.]=>2
[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]=>[.,[[.,[[.,[[.,.],.]],.]],.]]=>0
[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]=>[[.,[.,[.,[[[.,.],.],.]]]],.]=>2
[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]=>[.,[.,[.,[[[[.,.],.],.],.]]]]=>2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]=>3
[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]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>3
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[.,[.,.]]]],.],.]]=>2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>3
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]=>2
[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]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]=>2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]=>2
[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]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]=>2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>3
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]=>3
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]=>2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]=>2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]=>2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]=>3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>4
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>4
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>3
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>3
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>3
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>4
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>5
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Description
The number of occurrences of the contiguous pattern [.,[.,[.,.]]] in a binary tree.
oeis:A001006 counts binary trees avoiding this pattern.
oeis:A001006 counts binary trees avoiding this pattern.
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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