Identifier
-
Mp00012:
Binary trees
—to Dyck path: up step, left tree, down step, right tree⟶
Dyck paths
St000659: Dyck paths ⟶ ℤ
Values
=>
Cc0010;cc-rep-0
Cc0005;cc-rep
[.,[.,.]]=>[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]=>1
[[[.,.],.],.]=>[1,1,1,0,0,0]=>1
[.,[.,[.,[.,.]]]]=>[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]=>1
[.,[[[.,.],.],.]]=>[1,0,1,1,1,0,0,0]=>1
[[.,.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0]=>1
[[.,.],[[.,.],.]]=>[1,1,0,0,1,1,0,0]=>2
[[.,[.,.]],[.,.]]=>[1,1,0,1,0,0,1,0]=>1
[[[.,.],.],[.,.]]=>[1,1,1,0,0,0,1,0]=>1
[[.,[.,[.,.]]],.]=>[1,1,0,1,0,1,0,0]=>1
[[.,[[.,.],.]],.]=>[1,1,0,1,1,0,0,0]=>2
[[[.,.],[.,.]],.]=>[1,1,1,0,0,1,0,0]=>1
[[[.,[.,.]],.],.]=>[1,1,1,0,1,0,0,0]=>1
[[[[.,.],.],.],.]=>[1,1,1,1,0,0,0,0]=>1
[.,[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,0,1,0]=>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]=>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]=>2
[.,[[.,[.,.]],[.,.]]]=>[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]=>2
[.,[[[.,.],[.,.]],.]]=>[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]=>1
[[.,.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,0,0]=>2
[[.,.],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,0,1,0]=>2
[[.,.],[[.,[.,.]],.]]=>[1,1,0,0,1,1,0,1,0,0]=>2
[[.,.],[[[.,.],.],.]]=>[1,1,0,0,1,1,1,0,0,0]=>2
[[.,[.,.]],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,0]=>1
[[.,[.,.]],[[.,.],.]]=>[1,1,0,1,0,0,1,1,0,0]=>2
[[[.,.],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,0]=>1
[[[.,.],.],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,0]=>2
[[.,[.,[.,.]]],[.,.]]=>[1,1,0,1,0,1,0,0,1,0]=>1
[[.,[[.,.],.]],[.,.]]=>[1,1,0,1,1,0,0,0,1,0]=>2
[[[.,.],[.,.]],[.,.]]=>[1,1,1,0,0,1,0,0,1,0]=>1
[[[.,[.,.]],.],[.,.]]=>[1,1,1,0,1,0,0,0,1,0]=>1
[[[[.,.],.],.],[.,.]]=>[1,1,1,1,0,0,0,0,1,0]=>1
[[.,[.,[.,[.,.]]]],.]=>[1,1,0,1,0,1,0,1,0,0]=>1
[[.,[.,[[.,.],.]]],.]=>[1,1,0,1,0,1,1,0,0,0]=>2
[[.,[[.,.],[.,.]]],.]=>[1,1,0,1,1,0,0,1,0,0]=>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]=>1
[[[.,.],[[.,.],.]],.]=>[1,1,1,0,0,1,1,0,0,0]=>2
[[[.,[.,.]],[.,.]],.]=>[1,1,1,0,1,0,0,1,0,0]=>1
[[[[.,.],.],[.,.]],.]=>[1,1,1,1,0,0,0,1,0,0]=>1
[[[.,[.,[.,.]]],.],.]=>[1,1,1,0,1,0,1,0,0,0]=>1
[[[.,[[.,.],.]],.],.]=>[1,1,1,0,1,1,0,0,0,0]=>2
[[[[.,.],[.,.]],.],.]=>[1,1,1,1,0,0,1,0,0,0]=>1
[[[[.,[.,.]],.],.],.]=>[1,1,1,1,0,1,0,0,0,0]=>1
[[[[[.,.],.],.],.],.]=>[1,1,1,1,1,0,0,0,0,0]=>1
[.,[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>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]=>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]=>2
[.,[.,[[.,[.,.]],[.,.]]]]=>[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]=>2
[.,[.,[[[.,.],[.,.]],.]]]=>[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]=>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]=>2
[.,[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>2
[.,[[.,[.,.]],[.,[.,.]]]]=>[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]=>2
[.,[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>1
[.,[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>2
[.,[[.,[.,[.,.]]],[.,.]]]=>[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]=>2
[.,[[[.,.],[.,.]],[.,.]]]=>[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]=>2
[.,[[.,[[.,.],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>2
[.,[[.,[[.,[.,.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>2
[.,[[.,[[[.,.],.],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>2
[.,[[[.,.],[.,[.,.]]],.]]=>[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]=>2
[.,[[[.,[.,.]],[.,.]],.]]=>[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]=>2
[.,[[[[.,.],[.,.]],.],.]]=>[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]=>1
[[.,.],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>2
[[.,.],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>2
[[.,.],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>2
[[.,.],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>2
[[.,.],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>2
[[.,.],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>3
[[.,.],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>2
[[.,.],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>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]=>3
[[.,.],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>2
[[.,.],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>2
[[.,.],[[[[.,.],.],.],.]]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>2
[[.,[.,.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>1
[[.,[.,.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>2
[[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>2
[[.,[.,.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>2
[[.,[.,.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>2
[[[.,.],.],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>1
[[[.,.],.],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>2
[[[.,.],.],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>2
[[[.,.],.],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>2
[[[.,.],.],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>2
[[.,[.,[.,.]]],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[[.,[.,[.,.]]],[[.,.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>2
[[.,[[.,.],.]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>2
[[.,[[.,.],.]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>3
[[[.,.],[.,.]],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>1
[[[.,.],[.,.]],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>2
[[[.,[.,.]],.],[.,[.,.]]]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>1
[[[.,[.,.]],.],[[.,.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>2
[[[[.,.],.],.],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>1
[[[[.,.],.],.],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>2
[[.,[.,[.,[.,.]]]],[.,.]]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[[.,[.,[[.,.],.]]],[.,.]]=>[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]=>1
[[[.,.],[[.,.],.]],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>2
[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>1
[[[[.,.],.],[.,.]],[.,.]]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>1
[[[.,[.,[.,.]]],.],[.,.]]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>1
[[[.,[[.,.],.]],.],[.,.]]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>2
[[[[.,.],[.,.]],.],[.,.]]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>1
[[[[.,[.,.]],.],.],[.,.]]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>1
[[[[[.,.],.],.],.],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[[.,[.,[.,[.,[.,.]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>1
[[.,[.,[.,[[.,.],.]]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>2
[[.,[.,[[.,.],[.,.]]]],.]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>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]=>3
[[.,[[.,[.,.]],[.,.]]],.]=>[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]=>3
[[.,[[[.,.],[.,.]],.]],.]=>[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]=>1
[[[.,.],[.,[[.,.],.]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>2
[[[.,.],[[.,.],[.,.]]],.]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>2
[[[.,.],[[.,[.,.]],.]],.]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>2
[[[.,.],[[[.,.],.],.]],.]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>2
[[[.,[.,.]],[.,[.,.]]],.]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>1
[[[.,[.,.]],[[.,.],.]],.]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>2
[[[[.,.],.],[.,[.,.]]],.]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>1
[[[[.,.],.],[[.,.],.]],.]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>2
[[[.,[.,[.,.]]],[.,.]],.]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>1
[[[.,[[.,.],.]],[.,.]],.]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>2
[[[[.,.],[.,.]],[.,.]],.]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>1
[[[[.,[.,.]],.],[.,.]],.]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>1
[[[[[.,.],.],.],[.,.]],.]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[[[.,[.,[.,[.,.]]]],.],.]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>1
[[[.,[.,[[.,.],.]]],.],.]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>2
[[[.,[[.,.],[.,.]]],.],.]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>2
[[[.,[[.,[.,.]],.]],.],.]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>2
[[[.,[[[.,.],.],.]],.],.]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[[[[.,.],[.,[.,.]]],.],.]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>1
[[[[.,.],[[.,.],.]],.],.]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[[[[.,[.,.]],[.,.]],.],.]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[[[[[.,.],.],[.,.]],.],.]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[[[[.,[.,[.,.]]],.],.],.]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[[[[.,[[.,.],.]],.],.],.]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[[[[[.,.],[.,.]],.],.],.]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[[[[[.,[.,.]],.],.],.],.]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[[[[[[.,.],.],.],.],.],.]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>1
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>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]=>2
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[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]=>2
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[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]=>2
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>2
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>2
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>2
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[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]=>2
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>1
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>2
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[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]=>2
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[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]=>2
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>2
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>2
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[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]=>2
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[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]=>2
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[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]=>2
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>2
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>2
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>2
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>2
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>3
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>2
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>2
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>2
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>3
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>2
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>2
[.,[[.,.],[[[[.,.],.],.],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>2
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>2
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>2
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>2
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>2
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[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]=>2
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>2
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>2
[.,[[[.,.],.],[[[.,.],.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>2
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[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]=>2
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>2
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>3
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[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]=>2
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>1
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>2
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[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]=>2
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[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]=>2
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>2
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>2
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>2
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[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]=>2
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[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]=>2
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[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]=>2
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>2
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>2
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>2
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>3
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>2
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>2
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>3
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>2
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>2
[.,[[.,[[[[.,.],.],.],.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>2
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[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]=>2
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>2
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>2
[.,[[[.,.],[[[.,.],.],.]],.]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>2
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[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]=>2
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>1
[.,[[[[.,.],.],[[.,.],.]],.]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>2
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>1
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>2
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[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]=>2
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>2
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>2
[.,[[[.,[[[.,.],.],.]],.],.]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>2
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>1
[.,[[[[.,.],[[.,.],.]],.],.]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>2
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>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]=>2
[.,[[[[[.,.],[.,.]],.],.],.]]=>[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]=>1
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>2
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>2
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>2
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>3
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>2
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>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]=>3
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>2
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>2
[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>2
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>2
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>3
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>3
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>3
[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>3
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>2
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>3
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>2
[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>3
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>2
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>3
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>2
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>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]=>3
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>3
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>3
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>3
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>2
[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>3
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>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]=>3
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>2
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>2
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>2
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>2
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>2
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>2
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>3
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>2
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>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]=>3
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[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]=>1
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>2
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>2
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>2
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>2
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>2
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>3
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>2
[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>2
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>2
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>3
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>2
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>2
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>2
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>2
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>2
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>2
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>3
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>3
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>3
[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>3
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>1
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>2
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>2
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>2
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>2
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>1
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>2
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>2
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>2
[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>2
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>1
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>2
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>2
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>2
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>2
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>2
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>3
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>2
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>3
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>2
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>3
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>2
[[.,[[[.,.],.],.]],[[.,.],.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>3
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>1
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>2
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>2
[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>3
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>1
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>2
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>1
[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>2
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>1
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>2
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>2
[[[.,[[.,.],.]],.],[[.,.],.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>3
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>1
[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>2
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>1
[[[[.,[.,.]],.],.],[[.,.],.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>2
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>1
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>2
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[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]=>3
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[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]=>3
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[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]=>1
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>2
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>2
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>2
[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>2
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>1
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>2
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>1
[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>2
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>1
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>2
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>1
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>1
[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>1
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>1
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>2
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>2
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>2
[[[.,[[[.,.],.],.]],.],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>2
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>1
[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>2
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>1
[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>1
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>1
[[[[.,[[.,.],.]],.],.],[.,.]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>2
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>1
[[[[[.,[.,.]],.],.],.],[.,.]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>1
[[[[[[.,.],.],.],.],.],[.,.]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>1
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>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]=>3
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[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]=>3
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[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]=>3
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>3
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>3
[[.,[[.,.],[[[.,.],.],.]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>3
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>3
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>2
[[.,[[[.,.],.],[[.,.],.]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>3
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>3
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[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]=>3
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>3
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>3
[[.,[[.,[[[.,.],.],.]],.]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>3
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>2
[[.,[[[.,.],[[.,.],.]],.]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>3
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>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]=>3
[[.,[[[[.,.],[.,.]],.],.]],.]=>[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]=>1
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>2
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>2
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>2
[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>2
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>2
[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>3
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>2
[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>2
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>2
[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>3
[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>2
[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>2
[[[.,.],[[[[.,.],.],.],.]],.]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>2
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>1
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>2
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>2
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>2
[[[.,[.,.]],[[[.,.],.],.]],.]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>2
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>1
[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>2
[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>2
[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>2
[[[[.,.],.],[[[.,.],.],.]],.]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>2
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>1
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>2
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>2
[[[.,[[.,.],.]],[[.,.],.]],.]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>3
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>1
[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>2
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>1
[[[[.,[.,.]],.],[[.,.],.]],.]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>2
[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>1
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>2
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>1
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>2
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>2
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>2
[[[.,[[[.,.],.],.]],[.,.]],.]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>2
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>1
[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>2
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>1
[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>1
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>1
[[[[.,[[.,.],.]],.],[.,.]],.]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>2
[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>1
[[[[[.,[.,.]],.],.],[.,.]],.]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>1
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>1
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>1
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>2
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>2
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>2
[[[.,[.,[[[.,.],.],.]]],.],.]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>2
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>2
[[[.,[[.,.],[[.,.],.]]],.],.]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>3
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>2
[[[.,[[[.,.],.],[.,.]]],.],.]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>2
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>2
[[[.,[[.,[[.,.],.]],.]],.],.]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>3
[[[.,[[[.,.],[.,.]],.]],.],.]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>2
[[[.,[[[.,[.,.]],.],.]],.],.]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>2
[[[.,[[[[.,.],.],.],.]],.],.]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>2
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>1
[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>2
[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>2
[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>2
[[[[.,.],[[[.,.],.],.]],.],.]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>2
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>1
[[[[.,[.,.]],[[.,.],.]],.],.]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>2
[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>1
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>2
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>1
[[[[.,[[.,.],.]],[.,.]],.],.]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>2
[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>1
[[[[[.,[.,.]],.],[.,.]],.],.]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>1
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>1
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>1
[[[[.,[.,[[.,.],.]]],.],.],.]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>2
[[[[.,[[.,.],[.,.]]],.],.],.]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>2
[[[[.,[[.,[.,.]],.]],.],.],.]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>2
[[[[.,[[[.,.],.],.]],.],.],.]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>2
[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>1
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>2
[[[[[.,[.,.]],[.,.]],.],.],.]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>1
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>1
[[[[[.,[.,[.,.]]],.],.],.],.]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>1
[[[[[.,[[.,.],.]],.],.],.],.]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>2
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>1
[[[[[[.,[.,.]],.],.],.],.],.]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>1
[[[[[[[.,.],.],.],.],.],.],.]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>1
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>1
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>1
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[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]=>1
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>1
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>1
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>1
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>1
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>1
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>2
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>2
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>2
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>2
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>2
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>1
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>2
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>2
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>1
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>1
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>1
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>2
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>2
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>1
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>2
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>1
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>1
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>1
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>2
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>1
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>1
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>1
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[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
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>2
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>2
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>2
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>3
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>2
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>2
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>2
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>3
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>2
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>2
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>2
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>2
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>2
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>2
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>2
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>1
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>2
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>2
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>2
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>2
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>2
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>2
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>3
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>1
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>2
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>1
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>2
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>1
[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>2
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>2
[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>2
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>2
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>2
[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>1
[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>2
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>1
[.,[.,[[[[.,.],.],[.,.]],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>1
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>1
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>2
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>1
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>1
[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>1
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>2
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>2
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>2
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>3
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>2
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>2
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>3
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>2
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>2
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>2
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>1
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>2
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>2
[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>2
[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>2
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>1
[.,[.,[[[.,[.,.]],[[.,.],.]],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>2
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>1
[.,[.,[[[[.,.],.],[[.,.],.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>2
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>1
[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>2
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>1
[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>1
[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>1
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>1
[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>2
[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>2
[.,[.,[[[.,[[.,[.,.]],.]],.],.]]]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>2
[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>2
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>1
[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>2
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>1
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>1
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>1
[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>2
[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>1
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>1
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>1
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>2
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>2
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>2
[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>3
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>2
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>2
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>3
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>2
[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>2
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>2
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>2
[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>3
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>3
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>3
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>3
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>2
[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>3
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>2
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>3
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>2
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>3
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>2
[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>2
[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>2
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>3
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>3
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>3
[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>3
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>2
[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>3
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>2
[.,[[.,.],[[[[.,.],.],[.,.]],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>2
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>2
[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>3
[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>2
[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>2
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>2
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>2
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>2
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>2
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>3
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>2
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>2
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>3
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>2
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>2
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>2
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>1
[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>2
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>2
[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>2
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>2
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>2
[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>3
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>2
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>2
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>2
[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>3
[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>2
[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>2
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>2
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>2
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>2
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>2
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>3
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>3
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>3
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>3
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>1
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>2
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>2
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>2
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>2
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>1
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>2
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>2
[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>2
[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>2
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>1
[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>2
[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>2
[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>2
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>2
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>2
[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>3
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>2
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>3
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>2
[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>3
[.,[[.,[[[.,.],.],.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>2
[.,[[.,[[[.,.],.],.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>3
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>1
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>2
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>2
[.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>3
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>1
[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>2
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>1
[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>2
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>1
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>2
[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>2
[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>3
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>1
[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>2
[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>1
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>2
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>1
[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>2
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>2
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>2
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>2
[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>2
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>2
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>3
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>2
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>2
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>2
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>3
[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>2
[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>2
[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>2
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>1
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>2
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>2
[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>2
[.,[[[.,.],[[[.,.],.],.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>2
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>1
[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>2
[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>1
[.,[[[[.,.],.],[[.,.],.]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>2
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>1
[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>2
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>1
[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>1
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>1
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>1
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>2
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>2
[.,[[[.,[[.,[.,.]],.]],.],[.,.]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>2
[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>2
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>1
[.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>2
[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>1
[.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>1
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>1
[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>2
[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>1
[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>1
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>1
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>2
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[.,[[.,[.,[[.,.],[[.,.],.]]]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>3
[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>2
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>3
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>2
[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>2
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>2
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[.,[[.,[[.,.],[.,[[.,.],.]]]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>3
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>3
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>3
[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>3
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>3
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>2
[.,[[.,[[[.,.],.],[[.,.],.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>3
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>3
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>2
[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>2
[.,[[.,[[[[.,.],.],.],[.,.]]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>2
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>3
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>3
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>3
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>3
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>2
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>3
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>2
[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>2
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>2
[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>3
[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>2
[.,[[.,[[[[.,[.,.]],.],.],.]],.]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>2
[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>2
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>1
[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>2
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>2
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>2
[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>2
[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>2
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>3
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>2
[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>2
[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>2
[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>3
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>2
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>2
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>2
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>1
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>2
[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>2
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>2
[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>2
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>1
[.,[[[[.,.],.],[.,[[.,.],.]]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>2
[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>2
[.,[[[[.,.],.],[[.,[.,.]],.]],.]]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>2
[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>2
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>1
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>2
[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>2
[.,[[[.,[[.,.],.]],[[.,.],.]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>3
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>1
[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>2
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>1
[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>2
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>1
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>2
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>1
[.,[[[.,[.,[[.,.],.]]],[.,.]],.]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>2
[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>2
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>2
[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>2
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>1
[.,[[[[.,.],[[.,.],.]],[.,.]],.]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>2
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>1
[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>1
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>1
[.,[[[[.,[[.,.],.]],.],[.,.]],.]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>2
[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>1
[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>1
[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>1
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>1
[.,[[[.,[.,[.,[[.,.],.]]]],.],.]]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>2
[.,[[[.,[.,[[.,.],[.,.]]]],.],.]]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>2
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>2
[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>2
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>2
[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>3
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>2
[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>2
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>2
[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>3
[.,[[[.,[[[.,.],[.,.]],.]],.],.]]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>2
[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>2
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>2
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>1
[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>2
[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>2
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>2
[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>2
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>1
[.,[[[[.,[.,.]],[[.,.],.]],.],.]]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>2
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>1
[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>2
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>1
[.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>2
[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>1
[.,[[[[[.,[.,.]],.],[.,.]],.],.]]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>1
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>1
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>1
[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>2
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>2
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>2
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>2
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>1
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>2
[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>1
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>1
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>1
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>2
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>1
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>1
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>1
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>2
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>2
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>2
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>2
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>3
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>2
[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>2
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>2
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>3
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>2
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>2
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>2
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>3
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>3
[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>3
[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>3
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>2
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>3
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>2
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>3
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>2
[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>3
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>2
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>2
[[.,.],[.,[[[[.,.],.],.],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>2
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>2
[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>3
[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>3
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>3
[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>3
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>2
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>3
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>2
[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>2
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>3
[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>2
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>2
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>2
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>2
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>3
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>3
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>3
[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>3
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>3
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>4
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>3
[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>3
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>3
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>4
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>3
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>3
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>3
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>2
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>3
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>3
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>3
[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>3
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>2
[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>3
[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>3
[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>3
[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>3
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>2
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>3
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>3
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>4
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>2
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>3
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>2
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>3
[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>2
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>3
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>2
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>3
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>3
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>3
[[.,.],[[.,[[[.,.],.],.]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>3
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>2
[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>3
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>2
[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>2
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>2
[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>3
[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>2
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>2
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>2
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>2
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>3
[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>3
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>3
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>3
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>3
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>4
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>3
[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>3
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>3
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>4
[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>3
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>3
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>3
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>2
[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>3
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>3
[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>3
[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>3
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>2
[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>3
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>2
[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>3
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2
[[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>3
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>2
[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>2
[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>2
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>3
[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>3
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>3
[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>3
[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>2
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>3
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>2
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>2
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>2
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>3
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>2
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>2
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>2
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>2
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>2
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>2
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>3
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>2
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>2
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>3
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>2
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>2
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>2
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>2
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Description
The number of rises of length at least 2 of a Dyck path.
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 $r$.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!