Identifier
-
Mp00012:
Binary trees
—to Dyck path: up step, left tree, down step, right tree⟶
Dyck paths
St000025: Dyck paths ⟶ ℤ (values match St000439The position of the first down step of a Dyck path.)
Values
=>
Cc0010;cc-rep-0
Cc0005;cc-rep
[.,.]=>[1,0]=>1
[.,[.,.]]=>[1,0,1,0]=>1
[[.,.],.]=>[1,1,0,0]=>2
[.,[.,[.,.]]]=>[1,0,1,0,1,0]=>1
[.,[[.,.],.]]=>[1,0,1,1,0,0]=>1
[[.,.],[.,.]]=>[1,1,0,0,1,0]=>2
[[.,[.,.]],.]=>[1,1,0,1,0,0]=>2
[[[.,.],.],.]=>[1,1,1,0,0,0]=>3
[.,[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0]=>1
[.,[.,[[.,.],.]]]=>[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]=>1
[.,[[[.,.],.],.]]=>[1,0,1,1,1,0,0,0]=>1
[[.,.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0]=>2
[[.,.],[[.,.],.]]=>[1,1,0,0,1,1,0,0]=>2
[[.,[.,.]],[.,.]]=>[1,1,0,1,0,0,1,0]=>2
[[[.,.],.],[.,.]]=>[1,1,1,0,0,0,1,0]=>3
[[.,[.,[.,.]]],.]=>[1,1,0,1,0,1,0,0]=>2
[[.,[[.,.],.]],.]=>[1,1,0,1,1,0,0,0]=>2
[[[.,.],[.,.]],.]=>[1,1,1,0,0,1,0,0]=>3
[[[.,[.,.]],.],.]=>[1,1,1,0,1,0,0,0]=>3
[[[[.,.],.],.],.]=>[1,1,1,1,0,0,0,0]=>4
[.,[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,0,1,0]=>1
[.,[.,[.,[[.,.],.]]]]=>[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]=>1
[.,[.,[[[.,.],.],.]]]=>[1,0,1,0,1,1,1,0,0,0]=>1
[.,[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,0,1,0,1,0]=>1
[.,[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,0]=>1
[.,[[.,[.,.]],[.,.]]]=>[1,0,1,1,0,1,0,0,1,0]=>1
[.,[[[.,.],.],[.,.]]]=>[1,0,1,1,1,0,0,0,1,0]=>1
[.,[[.,[.,[.,.]]],.]]=>[1,0,1,1,0,1,0,1,0,0]=>1
[.,[[.,[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,0,0]=>1
[.,[[[.,.],[.,.]],.]]=>[1,0,1,1,1,0,0,1,0,0]=>1
[.,[[[.,[.,.]],.],.]]=>[1,0,1,1,1,0,1,0,0,0]=>1
[.,[[[[.,.],.],.],.]]=>[1,0,1,1,1,1,0,0,0,0]=>1
[[.,.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,0,1,0]=>2
[[.,.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,0,0]=>2
[[.,.],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,0,1,0]=>2
[[.,.],[[.,[.,.]],.]]=>[1,1,0,0,1,1,0,1,0,0]=>2
[[.,.],[[[.,.],.],.]]=>[1,1,0,0,1,1,1,0,0,0]=>2
[[.,[.,.]],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,0]=>2
[[.,[.,.]],[[.,.],.]]=>[1,1,0,1,0,0,1,1,0,0]=>2
[[[.,.],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,0]=>3
[[[.,.],.],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,0]=>3
[[.,[.,[.,.]]],[.,.]]=>[1,1,0,1,0,1,0,0,1,0]=>2
[[.,[[.,.],.]],[.,.]]=>[1,1,0,1,1,0,0,0,1,0]=>2
[[[.,.],[.,.]],[.,.]]=>[1,1,1,0,0,1,0,0,1,0]=>3
[[[.,[.,.]],.],[.,.]]=>[1,1,1,0,1,0,0,0,1,0]=>3
[[[[.,.],.],.],[.,.]]=>[1,1,1,1,0,0,0,0,1,0]=>4
[[.,[.,[.,[.,.]]]],.]=>[1,1,0,1,0,1,0,1,0,0]=>2
[[.,[.,[[.,.],.]]],.]=>[1,1,0,1,0,1,1,0,0,0]=>2
[[.,[[.,.],[.,.]]],.]=>[1,1,0,1,1,0,0,1,0,0]=>2
[[.,[[.,[.,.]],.]],.]=>[1,1,0,1,1,0,1,0,0,0]=>2
[[.,[[[.,.],.],.]],.]=>[1,1,0,1,1,1,0,0,0,0]=>2
[[[.,.],[.,[.,.]]],.]=>[1,1,1,0,0,1,0,1,0,0]=>3
[[[.,.],[[.,.],.]],.]=>[1,1,1,0,0,1,1,0,0,0]=>3
[[[.,[.,.]],[.,.]],.]=>[1,1,1,0,1,0,0,1,0,0]=>3
[[[[.,.],.],[.,.]],.]=>[1,1,1,1,0,0,0,1,0,0]=>4
[[[.,[.,[.,.]]],.],.]=>[1,1,1,0,1,0,1,0,0,0]=>3
[[[.,[[.,.],.]],.],.]=>[1,1,1,0,1,1,0,0,0,0]=>3
[[[[.,.],[.,.]],.],.]=>[1,1,1,1,0,0,1,0,0,0]=>4
[[[[.,[.,.]],.],.],.]=>[1,1,1,1,0,1,0,0,0,0]=>4
[[[[[.,.],.],.],.],.]=>[1,1,1,1,1,0,0,0,0,0]=>5
[.,[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>1
[.,[.,[.,[.,[[.,.],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>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]=>1
[.,[.,[.,[[[.,.],.],.]]]]=>[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]=>1
[.,[.,[[.,.],[[.,.],.]]]]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>1
[.,[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>1
[.,[.,[[[.,.],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>1
[.,[.,[[.,[.,[.,.]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[.,[.,[[.,[[.,.],.]],.]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>1
[.,[.,[[[.,.],[.,.]],.]]]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>1
[.,[.,[[[.,[.,.]],.],.]]]=>[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]=>1
[.,[[.,.],[.,[.,[.,.]]]]]=>[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]=>1
[.,[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>1
[.,[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>1
[.,[[.,.],[[[.,.],.],.]]]=>[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]=>1
[.,[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>1
[.,[[[.,.],.],[.,[.,.]]]]=>[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
[.,[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>1
[.,[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>1
[.,[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>1
[.,[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>1
[.,[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>1
[.,[[.,[.,[.,[.,.]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[.,[[.,[.,[[.,.],.]]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>1
[.,[[.,[[.,.],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>1
[.,[[.,[[.,[.,.]],.]],.]]=>[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]=>1
[.,[[[.,.],[.,[.,.]]],.]]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>1
[.,[[[.,.],[[.,.],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>1
[.,[[[.,[.,.]],[.,.]],.]]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>1
[.,[[[[.,.],.],[.,.]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>1
[.,[[[.,[.,[.,.]]],.],.]]=>[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]=>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]=>1
[.,[[[[[.,.],.],.],.],.]]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[[.,.],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>2
[[.,.],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>2
[[.,.],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>2
[[.,.],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>2
[[.,.],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>2
[[.,.],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>2
[[.,.],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>2
[[.,.],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>2
[[.,.],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>2
[[.,.],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>2
[[.,.],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>2
[[.,.],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>2
[[.,.],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>2
[[.,.],[[[[.,.],.],.],.]]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>2
[[.,[.,.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>2
[[.,[.,.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>2
[[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>2
[[.,[.,.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>2
[[.,[.,.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>2
[[[.,.],.],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>3
[[[.,.],.],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>3
[[[.,.],.],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[[[.,.],.],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>3
[[[.,.],.],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[[.,[.,[.,.]]],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>2
[[.,[.,[.,.]]],[[.,.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>2
[[.,[[.,.],.]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>2
[[.,[[.,.],.]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>2
[[[.,.],[.,.]],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>3
[[[.,.],[.,.]],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>3
[[[.,[.,.]],.],[.,[.,.]]]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>3
[[[.,[.,.]],.],[[.,.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>3
[[[[.,.],.],.],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>4
[[[[.,.],.],.],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>4
[[.,[.,[.,[.,.]]]],[.,.]]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>2
[[.,[.,[[.,.],.]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>2
[[.,[[.,.],[.,.]]],[.,.]]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>2
[[.,[[.,[.,.]],.]],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>2
[[.,[[[.,.],.],.]],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>2
[[[.,.],[.,[.,.]]],[.,.]]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>3
[[[.,.],[[.,.],.]],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>3
[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>3
[[[[.,.],.],[.,.]],[.,.]]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>4
[[[.,[.,[.,.]]],.],[.,.]]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>3
[[[.,[[.,.],.]],.],[.,.]]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>3
[[[[.,.],[.,.]],.],[.,.]]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>4
[[[[.,[.,.]],.],.],[.,.]]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>4
[[[[[.,.],.],.],.],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>5
[[.,[.,[.,[.,[.,.]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>2
[[.,[.,[.,[[.,.],.]]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>2
[[.,[.,[[.,.],[.,.]]]],.]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>2
[[.,[.,[[.,[.,.]],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>2
[[.,[.,[[[.,.],.],.]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>2
[[.,[[.,.],[.,[.,.]]]],.]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>2
[[.,[[.,.],[[.,.],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>2
[[.,[[.,[.,.]],[.,.]]],.]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>2
[[.,[[[.,.],.],[.,.]]],.]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[[.,[[.,[.,[.,.]]],.]],.]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>2
[[.,[[.,[[.,.],.]],.]],.]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>2
[[.,[[[.,.],[.,.]],.]],.]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>2
[[.,[[[.,[.,.]],.],.]],.]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>2
[[.,[[[[.,.],.],.],.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>2
[[[.,.],[.,[.,[.,.]]]],.]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>3
[[[.,.],[.,[[.,.],.]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>3
[[[.,.],[[.,.],[.,.]]],.]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>3
[[[.,.],[[.,[.,.]],.]],.]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>3
[[[.,.],[[[.,.],.],.]],.]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>3
[[[.,[.,.]],[.,[.,.]]],.]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>3
[[[.,[.,.]],[[.,.],.]],.]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>3
[[[[.,.],.],[.,[.,.]]],.]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>4
[[[[.,.],.],[[.,.],.]],.]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>4
[[[.,[.,[.,.]]],[.,.]],.]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>3
[[[.,[[.,.],.]],[.,.]],.]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>3
[[[[.,.],[.,.]],[.,.]],.]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>4
[[[[.,[.,.]],.],[.,.]],.]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>4
[[[[[.,.],.],.],[.,.]],.]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>5
[[[.,[.,[.,[.,.]]]],.],.]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>3
[[[.,[.,[[.,.],.]]],.],.]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>3
[[[.,[[.,.],[.,.]]],.],.]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>3
[[[.,[[.,[.,.]],.]],.],.]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>3
[[[.,[[[.,.],.],.]],.],.]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>3
[[[[.,.],[.,[.,.]]],.],.]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>4
[[[[.,.],[[.,.],.]],.],.]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>4
[[[[.,[.,.]],[.,.]],.],.]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>4
[[[[[.,.],.],[.,.]],.],.]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>5
[[[[.,[.,[.,.]]],.],.],.]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>4
[[[[.,[[.,.],.]],.],.],.]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>4
[[[[[.,.],[.,.]],.],.],.]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>5
[[[[[.,[.,.]],.],.],.],.]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>5
[[[[[[.,.],.],.],.],.],.]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>6
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[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]=>1
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>1
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>1
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>1
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>1
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[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]=>1
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>1
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>1
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>1
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>1
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[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]=>1
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>1
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[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
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>1
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>1
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>1
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>1
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>1
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>1
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[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]=>1
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>1
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>1
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>1
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>1
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[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]=>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]=>1
[.,[.,[[[[[.,.],.],.],.],.]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>1
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>1
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>1
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>1
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[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]=>1
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>1
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>1
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>1
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>1
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>1
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>1
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[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]=>1
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>1
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>1
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>1
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>1
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[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]=>1
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>1
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[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
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>1
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>1
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[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
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>1
[.,[[[[.,.],.],.],[[.,.],.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>1
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>1
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>1
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>1
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>1
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>1
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>1
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>1
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>1
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>1
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>1
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>1
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>1
[.,[[[[[.,.],.],.],.],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>1
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>1
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>1
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[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]=>1
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>1
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>1
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>1
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>1
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[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]=>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]=>1
[.,[[.,[[[[.,.],.],.],.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>1
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>1
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>1
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>1
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[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]=>1
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>1
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>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]=>1
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>1
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>1
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>1
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>1
[.,[[[[[.,.],.],.],[.,.]],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>1
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[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]=>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]=>1
[.,[[[.,[[[.,.],.],.]],.],.]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>1
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[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]=>1
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>1
[.,[[[[[.,.],.],[.,.]],.],.]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>1
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>1
[.,[[[[.,[[.,.],.]],.],.],.]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>1
[.,[[[[[.,.],[.,.]],.],.],.]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>1
[.,[[[[[.,[.,.]],.],.],.],.]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>1
[.,[[[[[[.,.],.],.],.],.],.]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>1
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>2
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>2
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>2
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>2
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>2
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>2
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>2
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>2
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>2
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>2
[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>2
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>2
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>2
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>2
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>2
[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>2
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>2
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>2
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>2
[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>2
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>2
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>2
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>2
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>2
[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>2
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>2
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>2
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>2
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>2
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>2
[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>2
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>2
[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>2
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>2
[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>2
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>2
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>2
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>2
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>2
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>2
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>2
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>2
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>2
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>2
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>2
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>2
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>2
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>2
[[.,[.,.]],[[[[.,.],.],.],.]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>2
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>3
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>3
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>3
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>3
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>3
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>3
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>3
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>3
[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>3
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>3
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>3
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>3
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>3
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>3
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>2
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>2
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>2
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>2
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>2
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>2
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>2
[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>2
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>3
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>3
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>3
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>3
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>3
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>3
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>3
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>3
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>3
[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>3
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>4
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>4
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>4
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>4
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>4
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>2
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>2
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>2
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>2
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>2
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>2
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>2
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[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
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>3
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>3
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>3
[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>3
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>3
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>3
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>4
[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>4
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>3
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>3
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>3
[[[.,[[.,.],.]],.],[[.,.],.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>3
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>4
[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>4
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>4
[[[[.,[.,.]],.],.],[[.,.],.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>4
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>5
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>5
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>2
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>2
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>2
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>2
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>2
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>2
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>2
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>2
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>2
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>2
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>2
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>2
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>2
[[.,[[[[.,.],.],.],.]],[.,.]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>2
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>3
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>3
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>3
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>3
[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>3
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>3
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>3
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>4
[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>4
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>3
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>3
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>4
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>4
[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>5
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>3
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>3
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>3
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>3
[[[.,[[[.,.],.],.]],.],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>3
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>4
[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>4
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>4
[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>5
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>4
[[[[.,[[.,.],.]],.],.],[.,.]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>4
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>5
[[[[[.,[.,.]],.],.],.],[.,.]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>5
[[[[[[.,.],.],.],.],.],[.,.]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>6
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>2
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>2
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>2
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>2
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>2
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>2
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>2
[[.,[.,[[[[.,.],.],.],.]]],.]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>2
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>2
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>2
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>2
[[.,[[.,.],[[[.,.],.],.]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>2
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>2
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>2
[[.,[[[.,.],.],[[.,.],.]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>2
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>2
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>2
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>2
[[.,[[[[.,.],.],.],[.,.]]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>2
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>2
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>2
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[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]=>2
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>2
[[.,[[[.,.],[[.,.],.]],.]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>2
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>2
[[.,[[[[.,.],.],[.,.]],.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>2
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>2
[[.,[[[.,[[.,.],.]],.],.]],.]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>2
[[.,[[[[.,.],[.,.]],.],.]],.]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>2
[[.,[[[[.,[.,.]],.],.],.]],.]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>2
[[.,[[[[[.,.],.],.],.],.]],.]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>2
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>3
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>3
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>3
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>3
[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>3
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>3
[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>3
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>3
[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>3
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>3
[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>3
[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>3
[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>3
[[[.,.],[[[[.,.],.],.],.]],.]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>3
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>3
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>3
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>3
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>3
[[[.,[.,.]],[[[.,.],.],.]],.]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>3
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>4
[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>4
[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>4
[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>4
[[[[.,.],.],[[[.,.],.],.]],.]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>4
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>3
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>3
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>3
[[[.,[[.,.],.]],[[.,.],.]],.]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>3
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>4
[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>4
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>4
[[[[.,[.,.]],.],[[.,.],.]],.]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>4
[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>5
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>5
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>3
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>3
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>3
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>3
[[[.,[[[.,.],.],.]],[.,.]],.]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>3
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>4
[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>4
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>4
[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>5
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>4
[[[[.,[[.,.],.]],.],[.,.]],.]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>4
[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>5
[[[[[.,[.,.]],.],.],[.,.]],.]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>5
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>6
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>3
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>3
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>3
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>3
[[[.,[.,[[[.,.],.],.]]],.],.]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>3
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>3
[[[.,[[.,.],[[.,.],.]]],.],.]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>3
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>3
[[[.,[[[.,.],.],[.,.]]],.],.]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>3
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>3
[[[.,[[.,[[.,.],.]],.]],.],.]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>3
[[[.,[[[.,.],[.,.]],.]],.],.]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>3
[[[.,[[[.,[.,.]],.],.]],.],.]=>[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]=>3
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>4
[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>4
[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>4
[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>4
[[[[.,.],[[[.,.],.],.]],.],.]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>4
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>4
[[[[.,[.,.]],[[.,.],.]],.],.]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>4
[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>5
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>5
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>4
[[[[.,[[.,.],.]],[.,.]],.],.]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>4
[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>5
[[[[[.,[.,.]],.],[.,.]],.],.]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>5
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>6
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>4
[[[[.,[.,[[.,.],.]]],.],.],.]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>4
[[[[.,[[.,.],[.,.]]],.],.],.]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>4
[[[[.,[[.,[.,.]],.]],.],.],.]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>4
[[[[.,[[[.,.],.],.]],.],.],.]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>4
[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>5
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>5
[[[[[.,[.,.]],[.,.]],.],.],.]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>5
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>6
[[[[[.,[.,[.,.]]],.],.],.],.]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>5
[[[[[.,[[.,.],.]],.],.],.],.]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>5
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>6
[[[[[[.,[.,.]],.],.],.],.],.]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>6
[[[[[[[.,.],.],.],.],.],.],.]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>7
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Description
The number of initial rises of a Dyck path.
In other words, this is the height of the first peak of $D$.
In other words, this is the height of the first peak of $D$.
Map
to Dyck path: up step, left tree, down step, right tree
Description
Return the associated Dyck path, using the bijection 1L0R.
This is given recursively as follows:
This is given recursively as follows:
- a leaf is associated to the empty Dyck Word
- a tree with children $l,r$ is associated with the Dyck path described by 1L0R where $L$ and $R$ are respectively the Dyck words associated with the trees $l$ and $r$.
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