Identifier
-
Mp00029:
Dyck paths
—to binary tree: left tree, up step, right tree, down step⟶
Binary trees
St000161: Binary trees ⟶ ℤ
Values
=>
Cc0005;cc-rep-0
Cc0010;cc-rep
[1,0]=>[.,.]=>0
[1,0,1,0]=>[[.,.],.]=>0
[1,1,0,0]=>[.,[.,.]]=>1
[1,0,1,0,1,0]=>[[[.,.],.],.]=>0
[1,0,1,1,0,0]=>[[.,.],[.,.]]=>1
[1,1,0,0,1,0]=>[[.,[.,.]],.]=>1
[1,1,0,1,0,0]=>[.,[[.,.],.]]=>2
[1,1,1,0,0,0]=>[.,[.,[.,.]]]=>3
[1,0,1,0,1,0,1,0]=>[[[[.,.],.],.],.]=>0
[1,0,1,0,1,1,0,0]=>[[[.,.],.],[.,.]]=>1
[1,0,1,1,0,0,1,0]=>[[[.,.],[.,.]],.]=>1
[1,0,1,1,0,1,0,0]=>[[.,.],[[.,.],.]]=>2
[1,0,1,1,1,0,0,0]=>[[.,.],[.,[.,.]]]=>3
[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]=>[[.,[[.,.],.]],.]=>2
[1,1,0,1,0,1,0,0]=>[.,[[[.,.],.],.]]=>3
[1,1,0,1,1,0,0,0]=>[.,[[.,.],[.,.]]]=>4
[1,1,1,0,0,0,1,0]=>[[.,[.,[.,.]]],.]=>3
[1,1,1,0,0,1,0,0]=>[.,[[.,[.,.]],.]]=>4
[1,1,1,0,1,0,0,0]=>[.,[.,[[.,.],.]]]=>5
[1,1,1,1,0,0,0,0]=>[.,[.,[.,[.,.]]]]=>6
[1,0,1,0,1,0,1,0,1,0]=>[[[[[.,.],.],.],.],.]=>0
[1,0,1,0,1,0,1,1,0,0]=>[[[[.,.],.],.],[.,.]]=>1
[1,0,1,0,1,1,0,0,1,0]=>[[[[.,.],.],[.,.]],.]=>1
[1,0,1,0,1,1,0,1,0,0]=>[[[.,.],.],[[.,.],.]]=>2
[1,0,1,0,1,1,1,0,0,0]=>[[[.,.],.],[.,[.,.]]]=>3
[1,0,1,1,0,0,1,0,1,0]=>[[[[.,.],[.,.]],.],.]=>1
[1,0,1,1,0,0,1,1,0,0]=>[[[.,.],[.,.]],[.,.]]=>2
[1,0,1,1,0,1,0,0,1,0]=>[[[.,.],[[.,.],.]],.]=>2
[1,0,1,1,0,1,0,1,0,0]=>[[.,.],[[[.,.],.],.]]=>3
[1,0,1,1,0,1,1,0,0,0]=>[[.,.],[[.,.],[.,.]]]=>4
[1,0,1,1,1,0,0,0,1,0]=>[[[.,.],[.,[.,.]]],.]=>3
[1,0,1,1,1,0,0,1,0,0]=>[[.,.],[[.,[.,.]],.]]=>4
[1,0,1,1,1,0,1,0,0,0]=>[[.,.],[.,[[.,.],.]]]=>5
[1,0,1,1,1,1,0,0,0,0]=>[[.,.],[.,[.,[.,.]]]]=>6
[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]=>[[.,[.,.]],[[.,.],.]]=>3
[1,1,0,0,1,1,1,0,0,0]=>[[.,[.,.]],[.,[.,.]]]=>4
[1,1,0,1,0,0,1,0,1,0]=>[[[.,[[.,.],.]],.],.]=>2
[1,1,0,1,0,0,1,1,0,0]=>[[.,[[.,.],.]],[.,.]]=>3
[1,1,0,1,0,1,0,0,1,0]=>[[.,[[[.,.],.],.]],.]=>3
[1,1,0,1,0,1,0,1,0,0]=>[.,[[[[.,.],.],.],.]]=>4
[1,1,0,1,0,1,1,0,0,0]=>[.,[[[.,.],.],[.,.]]]=>5
[1,1,0,1,1,0,0,0,1,0]=>[[.,[[.,.],[.,.]]],.]=>4
[1,1,0,1,1,0,0,1,0,0]=>[.,[[[.,.],[.,.]],.]]=>5
[1,1,0,1,1,0,1,0,0,0]=>[.,[[.,.],[[.,.],.]]]=>6
[1,1,0,1,1,1,0,0,0,0]=>[.,[[.,.],[.,[.,.]]]]=>7
[1,1,1,0,0,0,1,0,1,0]=>[[[.,[.,[.,.]]],.],.]=>3
[1,1,1,0,0,0,1,1,0,0]=>[[.,[.,[.,.]]],[.,.]]=>4
[1,1,1,0,0,1,0,0,1,0]=>[[.,[[.,[.,.]],.]],.]=>4
[1,1,1,0,0,1,0,1,0,0]=>[.,[[[.,[.,.]],.],.]]=>5
[1,1,1,0,0,1,1,0,0,0]=>[.,[[.,[.,.]],[.,.]]]=>6
[1,1,1,0,1,0,0,0,1,0]=>[[.,[.,[[.,.],.]]],.]=>5
[1,1,1,0,1,0,0,1,0,0]=>[.,[[.,[[.,.],.]],.]]=>6
[1,1,1,0,1,0,1,0,0,0]=>[.,[.,[[[.,.],.],.]]]=>7
[1,1,1,0,1,1,0,0,0,0]=>[.,[.,[[.,.],[.,.]]]]=>8
[1,1,1,1,0,0,0,0,1,0]=>[[.,[.,[.,[.,.]]]],.]=>6
[1,1,1,1,0,0,0,1,0,0]=>[.,[[.,[.,[.,.]]],.]]=>7
[1,1,1,1,0,0,1,0,0,0]=>[.,[.,[[.,[.,.]],.]]]=>8
[1,1,1,1,0,1,0,0,0,0]=>[.,[.,[.,[[.,.],.]]]]=>9
[1,1,1,1,1,0,0,0,0,0]=>[.,[.,[.,[.,[.,.]]]]]=>10
[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]=>[[[[[.,.],.],.],.],[.,.]]=>1
[1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],.],.],[.,.]],.]=>1
[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]=>[[[[.,.],.],.],[.,[.,.]]]=>3
[1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[.,.],.],[.,.]],.],.]=>1
[1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[.,.],.],[.,.]],[.,.]]=>2
[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]=>[[[.,.],.],[[[.,.],.],.]]=>3
[1,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,.],.],[[.,.],[.,.]]]=>4
[1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,.],.],[.,[.,.]]],.]=>3
[1,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,.],.],[[.,[.,.]],.]]=>4
[1,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,.],.],[.,[[.,.],.]]]=>5
[1,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,.],.],[.,[.,[.,.]]]]=>6
[1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[.,.],[.,.]],.],.],.]=>1
[1,0,1,1,0,0,1,0,1,1,0,0]=>[[[[.,.],[.,.]],.],[.,.]]=>2
[1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,.]],[.,.]],.]=>2
[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]=>[[[.,.],[.,.]],[.,[.,.]]]=>4
[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]=>[[[.,.],[[[.,.],.],.]],.]=>3
[1,0,1,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[.,.],.],.],.]]=>4
[1,0,1,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,.],.],[.,.]]]=>5
[1,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,.],[.,.]]],.]=>4
[1,0,1,1,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,.],[.,.]],.]]=>5
[1,0,1,1,0,1,1,0,1,0,0,0]=>[[.,.],[[.,.],[[.,.],.]]]=>6
[1,0,1,1,0,1,1,1,0,0,0,0]=>[[.,.],[[.,.],[.,[.,.]]]]=>7
[1,0,1,1,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,.]]],.],.]=>3
[1,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,.]]],[.,.]]=>4
[1,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,.]],.]],.]=>4
[1,0,1,1,1,0,0,1,0,1,0,0]=>[[.,.],[[[.,[.,.]],.],.]]=>5
[1,0,1,1,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[.,.]],[.,.]]]=>6
[1,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,.],[.,[[.,.],.]]],.]=>5
[1,0,1,1,1,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,.],.]],.]]=>6
[1,0,1,1,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[.,.],.],.]]]=>7
[1,0,1,1,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[.,.],[.,.]]]]=>8
[1,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,.]]]],.]=>6
[1,0,1,1,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[.,[.,.]]],.]]=>7
[1,0,1,1,1,1,0,0,1,0,0,0]=>[[.,.],[.,[[.,[.,.]],.]]]=>8
[1,0,1,1,1,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[.,.],.]]]]=>9
[1,0,1,1,1,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,.]]]]]=>10
[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]=>[[[.,[.,.]],.],[[.,.],.]]=>3
[1,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,.]],.],[.,[.,.]]]=>4
[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]=>[[[.,[.,.]],[[.,.],.]],.]=>3
[1,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,.],.],.]]=>4
[1,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,.]],[[.,.],[.,.]]]=>5
[1,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,.]]],.]=>4
[1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,.]],.]]=>5
[1,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[.,.],.]]]=>6
[1,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,.]]]]=>7
[1,1,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[.,.],.]],.],.],.]=>2
[1,1,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[.,.],.]],.],[.,.]]=>3
[1,1,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],.]],[.,.]],.]=>3
[1,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,.],.]],[[.,.],.]]=>4
[1,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[[.,.],.]],[.,[.,.]]]=>5
[1,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[.,.],.],.]],.],.]=>3
[1,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],.],.]],[.,.]]=>4
[1,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[.,.],.],.],.]],.]=>4
[1,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,.],.],.],.],.]]=>5
[1,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[.,.],.],.],[.,.]]]=>6
[1,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[.,.],.],[.,.]]],.]=>5
[1,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[.,.],.],[.,.]],.]]=>6
[1,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,.],.],[[.,.],.]]]=>7
[1,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[.,.],.],[.,[.,.]]]]=>8
[1,1,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[.,.],[.,.]]],.],.]=>4
[1,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[.,.]]],[.,.]]=>5
[1,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[.,.],[.,.]],.]],.]=>5
[1,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[.,.],[.,.]],.],.]]=>6
[1,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[.,.]],[.,.]]]=>7
[1,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,.],[[.,.],.]]],.]=>6
[1,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,.],.]],.]]=>7
[1,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[.,.],.],.]]]=>8
[1,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[.,.],[.,.]]]]=>9
[1,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[[.,.],[.,[.,.]]]],.]=>7
[1,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[[.,.],[.,[.,.]]],.]]=>8
[1,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[.,.]],.]]]=>9
[1,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[.,.],[.,[[.,.],.]]]]=>10
[1,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,.]]]]]=>11
[1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,.]]],.],.],.]=>3
[1,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[.,.]]],.],[.,.]]=>4
[1,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,.]]],[.,.]],.]=>4
[1,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,[.,.]]],[[.,.],.]]=>5
[1,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,.]]],[.,[.,.]]]=>6
[1,1,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[.,.]],.]],.],.]=>4
[1,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,.]],.]],[.,.]]=>5
[1,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[.,.]],.],.]],.]=>5
[1,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[.,.]],.],.],.]]=>6
[1,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,.]],.],[.,.]]]=>7
[1,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[.,.]]],.]=>6
[1,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[.,.]],.]]=>7
[1,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[.,.],.]]]=>8
[1,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[.,[.,.]],[.,[.,.]]]]=>9
[1,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[.,.],.]]],.],.]=>5
[1,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,.],.]]],[.,.]]=>6
[1,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,.],.]],.]],.]=>6
[1,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],.]],.],.]]=>7
[1,1,1,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],.]],[.,.]]]=>8
[1,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[.,.],.],.]]],.]=>7
[1,1,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[.,.],.],.]],.]]=>8
[1,1,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[.,.],.],.],.]]]=>9
[1,1,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[.,.],.],[.,.]]]]=>10
[1,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[.,.],[.,.]]]],.]=>8
[1,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[.,.],[.,.]]],.]]=>9
[1,1,1,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[.,.],[.,.]],.]]]=>10
[1,1,1,0,1,1,0,1,0,0,0,0]=>[.,[.,[[.,.],[[.,.],.]]]]=>11
[1,1,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,.]]]]]=>12
[1,1,1,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,.]]]],.],.]=>6
[1,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,.]]]],[.,.]]=>7
[1,1,1,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,.]]],.]],.]=>7
[1,1,1,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[.,.]]],.],.]]=>8
[1,1,1,1,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[.,.]]],[.,.]]]=>9
[1,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,.]],.]]],.]=>8
[1,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[.,.]],.]],.]]=>9
[1,1,1,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,.]],.],.]]]=>10
[1,1,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[.,.]],[.,.]]]]=>11
[1,1,1,1,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[.,.],.]]]],.]=>9
[1,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[.,.],.]]],.]]=>10
[1,1,1,1,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[.,.],.]],.]]]=>11
[1,1,1,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[.,.],.],.]]]]=>12
[1,1,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,.]]]]]=>13
[1,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,.]]]]],.]=>10
[1,1,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,.]]]],.]]=>11
[1,1,1,1,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,.]]],.]]]=>12
[1,1,1,1,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[.,.]],.]]]]=>13
[1,1,1,1,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],.]]]]]=>14
[1,1,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>15
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[.,.],.],.],.],.],[.,.]]=>1
[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]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>4
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[.,.],.],.],.],.]]=>5
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>11
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>4
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>6
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>5
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>6
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>11
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>12
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>11
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>11
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>12
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>13
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>11
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>12
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>13
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>14
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>15
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>4
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>5
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>11
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>5
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>4
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>6
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],.],.],.],.],.]]=>6
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>7
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>7
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[[.,.],.],[.,.]],.],.]]=>7
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>8
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[[.,.],[.,.]],.],.],.]]=>7
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>8
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>7
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>8
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>9
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>10
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[[[.,.],[[.,.],.]],.],.]]=>8
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>9
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>8
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]=>11
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>5
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[.,.]],.],.],.],.]]=>7
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[.,[.,.]],.],.],[.,.]]]=>8
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[.,[.,.]],[.,.]],.],.]]=>8
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>9
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[[.,.],.]],.],.],.]]=>8
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[.,.],.]],.],[.,.]]]=>9
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[[.,.],.],.]],.],.]]=>9
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[[.,.],.],.]],[.,.]]]=>10
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,.],.],.],.]],.]]=>10
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>11
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[.,[[.,.],[[.,.],.]]]],.]=>11
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]=>12
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[.,[.,.]]],.],.],.]]=>9
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[.,.]],.]],.],.]]=>10
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]=>11
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[[.,.],.]],.]]],.]=>11
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[[.,.],.],.]]]],.]=>12
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]=>13
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>11
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>11
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]=>12
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]=>13
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]=>14
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>15
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>1
[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]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>2
[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]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>2
[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]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>4
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>6
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>6
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>2
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>4
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>5
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>6
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>4
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]=>4
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>5
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>6
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>5
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>6
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>5
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>6
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>2
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>4
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>5
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>6
[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]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>5
[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]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>4
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>5
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>8
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>5
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>6
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>9
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>4
[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]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>4
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>6
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>8
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>8
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>8
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>8
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>8
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>10
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>12
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>12
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>12
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>5
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>6
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>5
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>6
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>6
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>7
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>8
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>9
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>8
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>10
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>11
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>12
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>10
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>12
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>12
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>12
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>18
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>18
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>19
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>18
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>19
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>20
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>21
[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]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>4
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>5
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>6
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>4
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>5
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>4
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>4
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>5
[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]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>6
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>6
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>7
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>8
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>6
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>8
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>8
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>9
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>10
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>11
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>6
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>8
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>8
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>10
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>10
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>10
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>12
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>10
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>12
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>3
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>4
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>6
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>7
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>7
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>8
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>8
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>8
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>4
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]=>7
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>8
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>10
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>8
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>8
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>8
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>10
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>10
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>11
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>12
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>12
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>13
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>14
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>8
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>12
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>12
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>4
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>6
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>8
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>9
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>10
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>10
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>11
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>12
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>6
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>8
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>8
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>8
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>7
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>8
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>9
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>10
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>11
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>12
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>10
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>8
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>9
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>10
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>10
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>12
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>14
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>12
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>12
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>10
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>10
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>12
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>12
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>14
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>12
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>16
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>18
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>16
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>18
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>19
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>18
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>19
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>20
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>21
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>28
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>28
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>36
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>27
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>27
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>36
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>45
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>35
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]=>26
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]=>26
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>26
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>26
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>35
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>45
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>8
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]=>9
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>9
[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]]=>14
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>10
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>10
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>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]=>[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]=>3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]]=>13
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>20
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]=>18
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]=>16
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]=>16
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]=>16
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]=>20
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]=>20
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]=>18
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]=>20
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]=>20
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]=>14
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]=>12
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]=>14
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]=>14
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]=>12
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]=>12
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]=>12
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]=>12
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]=>14
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]=>14
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]=>12
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]=>14
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]=>14
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]=>20
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]=>30
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]]=>28
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]]=>26
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]]=>26
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]]=>26
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]]=>24
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]]=>22
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]]=>22
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]]=>22
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]]=>24
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]]=>24
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]]=>22
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]]=>24
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]]=>24
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]]=>30
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]]=>30
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]]=>28
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]]=>30
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]]=>30
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.]]=>26
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.]]=>26
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]]=>26
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]]=>26
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]]=>30
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]]=>30
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]]=>28
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]]=>30
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]]=>30
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>22
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]=>20
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]=>18
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]=>18
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]=>18
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]=>22
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]=>22
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]=>20
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]=>22
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]=>22
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],[[.,.],.]]]]=>18
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],[[.,.],.]]]=>16
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],[[.,.],.]]],.]]=>18
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,[[.,[[.,.],.]],.]],.]]=>18
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],[[.,.],.]]]]=>18
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],[[.,.],.]]]=>16
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],[[.,.],.]]],.]]=>18
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,[[.,[[.,.],.]],.]],.]]=>18
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],[[.,.],.]]]=>18
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,[[.,.],.]],.]]=>18
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],[[.,.],.]]]=>18
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],.]]=>18
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],[[.,.],.]]]=>16
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,[[.,.],.]],.]]=>16
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],[[.,.],.]]]=>18
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,[[.,.],.]],.]]=>18
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],[[.,.],.]]]=>18
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,[[.,.],.]],.]]=>18
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],[[.,.],.]]=>22
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],[[.,.],.]]=>22
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],[[.,.],.]]=>20
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],[[.,.],.]]=>22
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],[[.,.],.]]=>22
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],[[.,.],.]]=>18
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],[[.,.],.]]=>18
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],[[.,.],.]]=>18
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],[[.,.],.]]=>18
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],[[.,.],.]]=>22
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],[[.,.],.]]=>22
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],[[.,.],.]]=>20
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],[[.,.],.]]=>22
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[[.,.],.]]=>22
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]=>7
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]=>9
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]=>11
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]=>13
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.]=>12
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>7
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]]=>9
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>11
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]]=>11
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>7
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]]=>11
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]]=>13
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]]=>15
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>17
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>7
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>9
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>13
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>9
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]]=>11
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]=>13
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]]=>17
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]=>13
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]]=>15
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]=>19
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]=>21
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]=>21
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]=>23
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]=>15
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]]=>17
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>25
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>17
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]]=>19
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>9
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>13
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>9
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>11
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>13
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>15
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>17
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]]=>19
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>11
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>15
[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]=>[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],[.,.]]=>8
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],[.,.]]=>12
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]=>8
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],[.,.]]=>10
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]]=>12
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],[.,.]]=>14
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],[.,.]]=>16
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],[.,.]]=>18
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>8
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>10
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],[.,.]]=>14
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]=>10
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],[.,.]]=>12
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]]=>12
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],[.,.]]=>14
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],[.,.]]=>18
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]]=>14
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],[.,.]]=>16
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],[.,.]]=>20
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],[.,.]]=>22
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],[.,.]]=>22
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],[.,.]]=>24
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]]=>16
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],[.,.]]=>18
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],[.,.]]=>26
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>18
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>20
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>8
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>10
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],[.,.]]=>14
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>10
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>12
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>14
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>16
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],[.,.]]=>18
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],[.,.]]=>20
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>10
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>12
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],[.,.]]=>16
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]=>12
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]]=>14
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]]=>12
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[[.,[[.,[.,.]],.]],.]]=>14
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[[.,[[.,[.,.]],.]],.]]=>18
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]=>14
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[[.,[[.,[.,.]],.]],.]]=>16
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]]=>18
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],.]]=>20
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],.]]=>22
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],.]]=>24
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]=>14
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]=>16
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],.]]=>20
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]]=>16
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],.]]=>18
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]=>20
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]=>22
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],.]]=>30
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]=>22
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]=>24
[1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]=>22
[1,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]=>24
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],.]]=>32
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]=>24
[1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]=>26
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],.]]=>24
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],.]]=>26
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],.]]=>26
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],.]]=>28
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],.]]=>34
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]]=>36
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],.]]=>26
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],.]]=>28
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.]]=>28
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],.]]=>30
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]=>16
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]=>18
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],.]]=>22
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]]=>18
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],.]]=>20
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>26
[1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>28
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],.]]=>30
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],.]]=>32
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>18
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>20
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],.]]=>24
[1,1,0,0,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]]=>20
[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],.]]=>22
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>8
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>10
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[[.,[.,.]],.]]=>14
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>10
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>12
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>14
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>16
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[[.,[.,.]],.]]=>18
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[[.,[.,.]],.]]=>20
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>10
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>12
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]]=>16
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>12
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>14
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>14
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>16
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]]=>20
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>16
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>18
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]]=>22
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]]=>24
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],.]]=>24
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],.]]=>26
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>18
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>20
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],.]]=>28
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]]=>20
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],.]]=>22
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]]=>10
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[[[.,[.,.]],[.,.]],.]]=>12
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[[[.,[.,.]],[.,.]],.]]=>16
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>12
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>14
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>16
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>18
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]]=>20
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],.]]=>22
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>12
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>14
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]]=>18
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]=>14
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]]=>16
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]=>7
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]]=>19
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]=>11
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]]=>17
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]]=>19
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],[[.,[[.,.],[.,.]]],.]]]=>24
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[[.,.],[.,.]]]]=>24
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]]=>25
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]]=>23
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Description
The sum of the sizes of the right subtrees of a binary tree.
This statistic corresponds to St000012The area of a Dyck path. under the Tamari Dyck path-binary tree bijection, and to St000018The number of inversions of a permutation. of the $312$-avoiding permutation corresponding to the binary tree.
It is also the sum of all heights $j$ of the coordinates $(i,j)$ of the Dyck path corresponding to the binary tree.
This statistic corresponds to St000012The area of a Dyck path. under the Tamari Dyck path-binary tree bijection, and to St000018The number of inversions of a permutation. of the $312$-avoiding permutation corresponding to the binary tree.
It is also the sum of all heights $j$ of the coordinates $(i,j)$ of the Dyck path corresponding to the binary tree.
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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