Identifier
-
Mp00020:
Binary trees
—to Tamari-corresponding Dyck path⟶
Dyck paths
St001037: Dyck paths ⟶ ℤ
Values
=>
Cc0010;cc-rep-0
Cc0005;cc-rep
[.,.]=>[1,0]=>0
[.,[.,.]]=>[1,1,0,0]=>0
[[.,.],.]=>[1,0,1,0]=>0
[.,[.,[.,.]]]=>[1,1,1,0,0,0]=>0
[.,[[.,.],.]]=>[1,1,0,1,0,0]=>0
[[.,.],[.,.]]=>[1,0,1,1,0,0]=>1
[[.,[.,.]],.]=>[1,1,0,0,1,0]=>0
[[[.,.],.],.]=>[1,0,1,0,1,0]=>0
[.,[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0]=>0
[.,[.,[[.,.],.]]]=>[1,1,1,0,1,0,0,0]=>0
[.,[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,0]=>0
[.,[[.,[.,.]],.]]=>[1,1,1,0,0,1,0,0]=>1
[.,[[[.,.],.],.]]=>[1,1,0,1,0,1,0,0]=>0
[[.,.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0]=>1
[[.,.],[[.,.],.]]=>[1,0,1,1,0,1,0,0]=>1
[[.,[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0]=>1
[[[.,.],.],[.,.]]=>[1,0,1,0,1,1,0,0]=>1
[[.,[.,[.,.]]],.]=>[1,1,1,0,0,0,1,0]=>0
[[.,[[.,.],.]],.]=>[1,1,0,1,0,0,1,0]=>0
[[[.,.],[.,.]],.]=>[1,0,1,1,0,0,1,0]=>1
[[[.,[.,.]],.],.]=>[1,1,0,0,1,0,1,0]=>0
[[[[.,.],.],.],.]=>[1,0,1,0,1,0,1,0]=>0
[.,[.,[.,[.,[.,.]]]]]=>[1,1,1,1,1,0,0,0,0,0]=>0
[.,[.,[.,[[.,.],.]]]]=>[1,1,1,1,0,1,0,0,0,0]=>0
[.,[.,[[.,.],[.,.]]]]=>[1,1,1,0,1,1,0,0,0,0]=>1
[.,[.,[[.,[.,.]],.]]]=>[1,1,1,1,0,0,1,0,0,0]=>0
[.,[.,[[[.,.],.],.]]]=>[1,1,1,0,1,0,1,0,0,0]=>0
[.,[[.,.],[.,[.,.]]]]=>[1,1,0,1,1,1,0,0,0,0]=>0
[.,[[.,.],[[.,.],.]]]=>[1,1,0,1,1,0,1,0,0,0]=>0
[.,[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,0,0,0]=>1
[.,[[[.,.],.],[.,.]]]=>[1,1,0,1,0,1,1,0,0,0]=>0
[.,[[.,[.,[.,.]]],.]]=>[1,1,1,1,0,0,0,1,0,0]=>1
[.,[[.,[[.,.],.]],.]]=>[1,1,1,0,1,0,0,1,0,0]=>1
[.,[[[.,.],[.,.]],.]]=>[1,1,0,1,1,0,0,1,0,0]=>1
[.,[[[.,[.,.]],.],.]]=>[1,1,1,0,0,1,0,1,0,0]=>1
[.,[[[[.,.],.],.],.]]=>[1,1,0,1,0,1,0,1,0,0]=>0
[[.,.],[.,[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,0]=>1
[[.,.],[.,[[.,.],.]]]=>[1,0,1,1,1,0,1,0,0,0]=>1
[[.,.],[[.,.],[.,.]]]=>[1,0,1,1,0,1,1,0,0,0]=>1
[[.,.],[[.,[.,.]],.]]=>[1,0,1,1,1,0,0,1,0,0]=>2
[[.,.],[[[.,.],.],.]]=>[1,0,1,1,0,1,0,1,0,0]=>1
[[.,[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0]=>1
[[.,[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,1,0,0]=>1
[[[.,.],.],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0]=>1
[[[.,.],.],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0]=>1
[[.,[.,[.,.]]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0]=>1
[[.,[[.,.],.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0]=>1
[[[.,.],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0]=>2
[[[.,[.,.]],.],[.,.]]=>[1,1,0,0,1,0,1,1,0,0]=>1
[[[[.,.],.],.],[.,.]]=>[1,0,1,0,1,0,1,1,0,0]=>1
[[.,[.,[.,[.,.]]]],.]=>[1,1,1,1,0,0,0,0,1,0]=>0
[[.,[.,[[.,.],.]]],.]=>[1,1,1,0,1,0,0,0,1,0]=>0
[[.,[[.,.],[.,.]]],.]=>[1,1,0,1,1,0,0,0,1,0]=>0
[[.,[[.,[.,.]],.]],.]=>[1,1,1,0,0,1,0,0,1,0]=>1
[[.,[[[.,.],.],.]],.]=>[1,1,0,1,0,1,0,0,1,0]=>0
[[[.,.],[.,[.,.]]],.]=>[1,0,1,1,1,0,0,0,1,0]=>1
[[[.,.],[[.,.],.]],.]=>[1,0,1,1,0,1,0,0,1,0]=>1
[[[.,[.,.]],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,0]=>1
[[[[.,.],.],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,0]=>1
[[[.,[.,[.,.]]],.],.]=>[1,1,1,0,0,0,1,0,1,0]=>0
[[[.,[[.,.],.]],.],.]=>[1,1,0,1,0,0,1,0,1,0]=>0
[[[[.,.],[.,.]],.],.]=>[1,0,1,1,0,0,1,0,1,0]=>1
[[[[.,[.,.]],.],.],.]=>[1,1,0,0,1,0,1,0,1,0]=>0
[[[[[.,.],.],.],.],.]=>[1,0,1,0,1,0,1,0,1,0]=>0
[.,[.,[.,[.,[.,[.,.]]]]]]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[.,[.,[.,[.,[[.,.],.]]]]]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>0
[.,[.,[.,[[.,.],[.,.]]]]]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>0
[.,[.,[.,[[.,[.,.]],.]]]]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[.,[.,[.,[[[.,.],.],.]]]]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>0
[.,[.,[[.,.],[.,[.,.]]]]]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[.,[.,[[.,.],[[.,.],.]]]]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>1
[.,[.,[[.,[.,.]],[.,.]]]]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[.,[.,[[[.,.],.],[.,.]]]]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>1
[.,[.,[[.,[.,[.,.]]],.]]]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>0
[.,[.,[[.,[[.,.],.]],.]]]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>0
[.,[.,[[[.,.],[.,.]],.]]]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[.,[.,[[[.,[.,.]],.],.]]]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>0
[.,[.,[[[[.,.],.],.],.]]]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>0
[.,[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>0
[.,[[.,.],[.,[[.,.],.]]]]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>0
[.,[[.,.],[[.,.],[.,.]]]]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>1
[.,[[.,.],[[.,[.,.]],.]]]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>0
[.,[[.,.],[[[.,.],.],.]]]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>0
[.,[[.,[.,.]],[.,[.,.]]]]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>1
[.,[[.,[.,.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>1
[.,[[[.,.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>0
[.,[[[.,.],.],[[.,.],.]]]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>0
[.,[[.,[.,[.,.]]],[.,.]]]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>1
[.,[[.,[[.,.],.]],[.,.]]]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>1
[.,[[[.,.],[.,.]],[.,.]]]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>1
[.,[[[.,[.,.]],.],[.,.]]]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>1
[.,[[[[.,.],.],.],[.,.]]]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>0
[.,[[.,[.,[.,[.,.]]]],.]]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[.,[[.,[.,[[.,.],.]]],.]]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>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
[.,[[.,[[[.,.],.],.]],.]]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>1
[.,[[[.,.],[.,[.,.]]],.]]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>1
[.,[[[.,.],[[.,.],.]],.]]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>1
[.,[[[.,[.,.]],[.,.]],.]]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>2
[.,[[[[.,.],.],[.,.]],.]]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>1
[.,[[[.,[.,[.,.]]],.],.]]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>1
[.,[[[.,[[.,.],.]],.],.]]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>1
[.,[[[[.,.],[.,.]],.],.]]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>1
[.,[[[[.,[.,.]],.],.],.]]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>1
[.,[[[[[.,.],.],.],.],.]]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>0
[[.,.],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[[.,.],[.,[.,[[.,.],.]]]]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>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
[[.,.],[.,[[[.,.],.],.]]]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>1
[[.,.],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>1
[[.,.],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>1
[[.,.],[[.,[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>2
[[.,.],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>1
[[.,.],[[.,[.,[.,.]]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>2
[[.,.],[[.,[[.,.],.]],.]]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>2
[[.,.],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>2
[[.,.],[[[.,[.,.]],.],.]]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>2
[[.,.],[[[[.,.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[[.,[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>1
[[.,[.,.]],[.,[[.,.],.]]]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>1
[[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>1
[[.,[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>2
[[.,[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>1
[[[.,.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>1
[[[.,.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>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]=>2
[[[.,.],.],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[[.,[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>1
[[.,[.,[.,.]]],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>1
[[.,[[.,.],.]],[.,[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>1
[[.,[[.,.],.]],[[.,.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>1
[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>2
[[[.,.],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>2
[[[.,[.,.]],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>1
[[[.,[.,.]],.],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>1
[[[[.,.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>1
[[[[.,.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>1
[[.,[.,[.,[.,.]]]],[.,.]]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>1
[[.,[.,[[.,.],.]]],[.,.]]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>1
[[.,[[.,.],[.,.]]],[.,.]]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>1
[[.,[[.,[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>2
[[.,[[[.,.],.],.]],[.,.]]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>1
[[[.,.],[.,[.,.]]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>2
[[[.,.],[[.,.],.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>2
[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>2
[[[[.,.],.],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>2
[[[.,[.,[.,.]]],.],[.,.]]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>1
[[[.,[[.,.],.]],.],[.,.]]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>1
[[[[.,.],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>2
[[[[.,[.,.]],.],.],[.,.]]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>1
[[[[[.,.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>1
[[.,[.,[.,[.,[.,.]]]]],.]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>0
[[.,[.,[.,[[.,.],.]]]],.]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>0
[[.,[.,[[.,.],[.,.]]]],.]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>1
[[.,[.,[[.,[.,.]],.]]],.]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>0
[[.,[.,[[[.,.],.],.]]],.]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>0
[[.,[[.,.],[.,[.,.]]]],.]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>0
[[.,[[.,.],[[.,.],.]]],.]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>0
[[.,[[.,[.,.]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>1
[[.,[[[.,.],.],[.,.]]],.]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>0
[[.,[[.,[.,[.,.]]],.]],.]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>1
[[.,[[.,[[.,.],.]],.]],.]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>1
[[.,[[[.,.],[.,.]],.]],.]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>1
[[.,[[[.,[.,.]],.],.]],.]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>1
[[.,[[[[.,.],.],.],.]],.]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>0
[[[.,.],[.,[.,[.,.]]]],.]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>1
[[[.,.],[.,[[.,.],.]]],.]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>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]=>2
[[[.,.],[[[.,.],.],.]],.]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>1
[[[.,[.,.]],[.,[.,.]]],.]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>1
[[[.,[.,.]],[[.,.],.]],.]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>1
[[[[.,.],.],[.,[.,.]]],.]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>1
[[[[.,.],.],[[.,.],.]],.]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>1
[[[.,[.,[.,.]]],[.,.]],.]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>1
[[[.,[[.,.],.]],[.,.]],.]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>1
[[[[.,.],[.,.]],[.,.]],.]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>2
[[[[.,[.,.]],.],[.,.]],.]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>1
[[[[[.,.],.],.],[.,.]],.]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>1
[[[.,[.,[.,[.,.]]]],.],.]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>0
[[[.,[.,[[.,.],.]]],.],.]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>0
[[[.,[[.,.],[.,.]]],.],.]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>0
[[[.,[[.,[.,.]],.]],.],.]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>1
[[[.,[[[.,.],.],.]],.],.]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>0
[[[[.,.],[.,[.,.]]],.],.]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>1
[[[[.,.],[[.,.],.]],.],.]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>1
[[[[.,[.,.]],[.,.]],.],.]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>1
[[[[[.,.],.],[.,.]],.],.]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>1
[[[[.,[.,[.,.]]],.],.],.]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>0
[[[[.,[[.,.],.]],.],.],.]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>0
[[[[[.,.],[.,.]],.],.],.]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>1
[[[[[.,[.,.]],.],.],.],.]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>0
[[[[[[.,.],.],.],.],.],.]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>0
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>0
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>1
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>0
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>0
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>0
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>0
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>1
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>0
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>1
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>1
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>1
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>1
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>0
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>1
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>1
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>1
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>2
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>1
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>1
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>1
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>1
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>1
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>1
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>1
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>2
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>1
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>1
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>0
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>0
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>0
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>1
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>0
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>1
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>1
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>1
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>1
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>0
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>0
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>1
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>0
[.,[.,[[[[[.,.],.],.],.],.]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>0
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>0
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>0
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>0
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>1
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>0
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>1
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>1
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>1
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>1
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>0
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>0
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>1
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>0
[.,[[.,.],[[[[.,.],.],.],.]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>0
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>1
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>1
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>2
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>1
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>1
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>0
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>0
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>1
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>0
[.,[[[.,.],.],[[[.,.],.],.]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>0
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>1
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>1
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>1
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>1
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>1
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>1
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>1
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>1
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>0
[.,[[[[.,.],.],.],[[.,.],.]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>0
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>1
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>1
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>2
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>1
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>1
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>1
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>1
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>2
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>1
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>1
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>1
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>1
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>1
[.,[[[[[.,.],.],.],.],[.,.]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>0
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>1
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>1
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>1
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>2
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>1
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>2
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>2
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>2
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>2
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>1
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>1
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>2
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>1
[.,[[.,[[[[.,.],.],.],.]],.]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>1
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>1
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>1
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[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]=>1
[.,[[[.,.],[[[.,.],.],.]],.]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>1
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>2
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>2
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>1
[.,[[[[.,.],.],[[.,.],.]],.]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>1
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>2
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>2
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>2
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>2
[.,[[[[[.,.],.],.],[.,.]],.]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>1
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>1
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>1
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>2
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>1
[.,[[[.,[[[.,.],.],.]],.],.]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>1
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>1
[.,[[[[.,.],[[.,.],.]],.],.]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>1
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>2
[.,[[[[[.,.],.],[.,.]],.],.]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>1
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>1
[.,[[[[.,[[.,.],.]],.],.],.]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>1
[.,[[[[[.,.],[.,.]],.],.],.]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>1
[.,[[[[[.,[.,.]],.],.],.],.]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>1
[.,[[[[[[.,.],.],.],.],.],.]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>0
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>1
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>1
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>1
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>2
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>1
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>2
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>2
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>2
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>2
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>1
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>1
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>2
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>1
[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>1
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>1
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>1
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>2
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>1
[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>1
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>2
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>2
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>1
[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>1
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>2
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>2
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>2
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>2
[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>1
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>2
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>2
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>3
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>2
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>2
[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>2
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>3
[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>2
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>2
[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>2
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>2
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>2
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>1
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>1
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>2
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>1
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>1
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>1
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>1
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>2
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>1
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>2
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>2
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>2
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>2
[[.,[.,.]],[[[[.,.],.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>1
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>1
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>1
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>2
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>1
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>1
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>1
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>1
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>2
[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>1
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>2
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>2
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>2
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>2
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>1
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>1
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>1
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>2
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>1
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>1
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>1
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>1
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>2
[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>1
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>2
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>2
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>2
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>3
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>2
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>1
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>1
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>1
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>2
[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>1
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>1
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>1
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>1
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>2
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>1
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>1
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>1
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>1
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>1
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>1
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>2
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>2
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>1
[[.,[[[.,.],.],.]],[[.,.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>1
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>2
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>2
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>2
[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>2
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>2
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>2
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>2
[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>2
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>1
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>1
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>1
[[[.,[[.,.],.]],.],[[.,.],.]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>1
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>2
[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>2
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>1
[[[[.,[.,.]],.],.],[[.,.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>1
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>1
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>1
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>1
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>2
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>1
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>1
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>1
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>1
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>2
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>1
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>2
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>2
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>2
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>2
[[.,[[[[.,.],.],.],.]],[.,.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>1
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>2
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>2
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>2
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>3
[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>2
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>2
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>2
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>2
[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>2
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>2
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>2
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>3
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>2
[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>2
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>1
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>1
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>1
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>2
[[[.,[[[.,.],.],.]],.],[.,.]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>1
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>2
[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>2
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>2
[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>2
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>1
[[[[.,[[.,.],.]],.],.],[.,.]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>1
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>2
[[[[[.,[.,.]],.],.],.],[.,.]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>1
[[[[[[.,.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>0
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>0
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>0
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>1
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>0
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>1
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>1
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>1
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>1
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>0
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>0
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>1
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>0
[[.,[.,[[[[.,.],.],.],.]]],.]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>0
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>0
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>0
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>1
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>0
[[.,[[.,.],[[[.,.],.],.]]],.]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>0
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>1
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>1
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>0
[[.,[[[.,.],.],[[.,.],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>0
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>1
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>1
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>1
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>1
[[.,[[[[.,.],.],.],[.,.]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>0
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>1
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>1
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>2
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>1
[[.,[[.,[[[.,.],.],.]],.]],.]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>1
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>1
[[.,[[[.,.],[[.,.],.]],.]],.]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>1
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>2
[[.,[[[[.,.],.],[.,.]],.]],.]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>1
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>1
[[.,[[[.,[[.,.],.]],.],.]],.]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>1
[[.,[[[[.,.],[.,.]],.],.]],.]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>1
[[.,[[[[.,[.,.]],.],.],.]],.]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>1
[[.,[[[[[.,.],.],.],.],.]],.]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>0
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>1
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>1
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>2
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>1
[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>1
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>1
[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>1
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>2
[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>1
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>2
[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>2
[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>2
[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>2
[[[.,.],[[[[.,.],.],.],.]],.]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>1
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>1
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>1
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>2
[[[.,[.,.]],[[[.,.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>1
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>1
[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>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]=>2
[[[[.,.],.],[[[.,.],.],.]],.]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>1
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>1
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>1
[[[.,[[.,.],.]],[[.,.],.]],.]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>1
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>2
[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>2
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>1
[[[[.,[.,.]],.],[[.,.],.]],.]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>1
[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>1
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>1
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>1
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>1
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>2
[[[.,[[[.,.],.],.]],[.,.]],.]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>1
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>2
[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>2
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>2
[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>2
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>1
[[[[.,[[.,.],.]],.],[.,.]],.]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>1
[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>2
[[[[[.,[.,.]],.],.],[.,.]],.]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>1
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>0
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>0
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>1
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>0
[[[.,[.,[[[.,.],.],.]]],.],.]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>0
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>0
[[[.,[[.,.],[[.,.],.]]],.],.]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>0
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>1
[[[.,[[[.,.],.],[.,.]]],.],.]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>0
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>1
[[[.,[[.,[[.,.],.]],.]],.],.]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>1
[[[.,[[[.,.],[.,.]],.]],.],.]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>1
[[[.,[[[.,[.,.]],.],.]],.],.]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>1
[[[.,[[[[.,.],.],.],.]],.],.]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>0
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>1
[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>1
[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>1
[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>2
[[[[.,.],[[[.,.],.],.]],.],.]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>1
[[[[.,[.,.]],[[.,.],.]],.],.]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>1
[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>1
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>1
[[[[.,[[.,.],.]],[.,.]],.],.]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>1
[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>2
[[[[[.,[.,.]],.],[.,.]],.],.]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>1
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>1
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>0
[[[[.,[.,[[.,.],.]]],.],.],.]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>0
[[[[.,[[.,.],[.,.]]],.],.],.]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>0
[[[[.,[[.,[.,.]],.]],.],.],.]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>1
[[[[.,[[[.,.],.],.]],.],.],.]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>0
[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>1
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[[[[[.,[.,.]],[.,.]],.],.],.]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>1
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>1
[[[[[.,[.,[.,.]]],.],.],.],.]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>0
[[[[[.,[[.,.],.]],.],.],.],.]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>0
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[[[[[[.,[.,.]],.],.],.],.],.]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>0
[[[[[[[.,.],.],.],.],.],.],.]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>1
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>1
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>2
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>1
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>1
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>1
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>1
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>2
[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>1
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>2
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>2
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>2
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>2
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>1
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>2
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>2
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>2
[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>3
[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>2
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>2
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>2
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>2
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>2
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>2
[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>2
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>3
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>2
[[.,.],[.,[[[[.,.],.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>2
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>1
[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>1
[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>1
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>2
[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>1
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>2
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>2
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>2
[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>2
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>1
[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>1
[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>2
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>1
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>1
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>1
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>1
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>1
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>2
[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>1
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>2
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>2
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>2
[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>2
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>1
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>1
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>2
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>1
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>1
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>2
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>2
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>3
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>2
[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>2
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>1
[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>1
[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>2
[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>1
[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>1
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>2
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>2
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>2
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>2
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>2
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>2
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>2
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>2
[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>1
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>1
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>2
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>2
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>3
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>2
[[.,.],[[.,[[[.,.],.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>2
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>2
[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>2
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>3
[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>2
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>2
[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>2
[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>2
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>2
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>1
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>2
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>2
[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[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]=>3
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>2
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>3
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>3
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>3
[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>3
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>2
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>2
[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>3
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>2
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>2
[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>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
[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>3
[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>3
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>2
[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>3
[[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>3
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>3
[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>3
[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>2
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>2
[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>3
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>2
[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2
[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>2
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>3
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>2
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>1
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>1
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>1
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>2
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>1
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>2
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>2
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>2
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>2
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>1
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>1
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>2
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>1
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>1
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>1
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>1
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>2
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>1
[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>1
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>2
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>2
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>1
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>1
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>2
[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>2
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>2
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>2
[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>1
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>2
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>2
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>3
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>2
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>2
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>2
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>3
[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>2
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>2
[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>2
[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>2
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>2
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>1
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>1
[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>1
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>2
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>1
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>2
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>2
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>2
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>2
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>1
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>1
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>2
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>1
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>1
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>1
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>1
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>2
[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>1
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>1
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>2
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>2
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>1
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>1
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>2
[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>2
[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>2
[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>2
[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>1
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>2
[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>2
[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>3
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>2
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>2
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>2
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>3
[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>2
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>2
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>2
[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>2
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>2
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>2
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>2
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>3
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>2
[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>2
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>2
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>2
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>3
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>2
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>3
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>3
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>3
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>3
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>1
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>1
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>2
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>1
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>1
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>1
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>1
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>2
[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>1
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>2
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>2
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>2
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>2
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>1
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>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
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>1
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>1
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>1
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>2
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>1
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>2
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>2
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>2
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>2
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>2
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>2
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>2
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>3
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>2
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>2
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>2
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>2
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>3
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>2
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>2
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>2
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>3
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>2
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>2
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>2
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>2
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>3
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>2
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>1
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>1
[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>1
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>2
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>1
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>2
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>2
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>2
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>3
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>1
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>1
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>1
[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>2
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>1
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>1
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>1
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>2
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>2
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>2
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>2
[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>2
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>2
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>2
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>3
[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>3
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>2
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>2
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>2
[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>2
[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>2
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>2
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>2
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>2
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>2
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>3
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>3
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>2
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>2
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>2
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>2
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>2
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>2
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>2
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>2
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>2
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>2
[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>2
[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>1
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>1
[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>2
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>1
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>1
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>2
[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>2
[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>3
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>2
[[[.,.],[.,[[[.,.],.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>2
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>2
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>2
[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>3
[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>2
[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>3
[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>3
[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>3
[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>3
[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>2
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>2
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>2
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>3
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>2
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>2
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>2
[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>2
[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>3
[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>2
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>3
[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>3
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>2
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>2
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>2
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>2
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>3
[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>3
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>3
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>3
[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>2
[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>3
[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>2
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>2
[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>2
[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>2
[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>2
[[[[.,.],[[.,[.,.]],.]],.],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>3
[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>2
[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>2
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>2
[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>2
[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>3
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>2
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>2
[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>2
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>2
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>2
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>1
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>1
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>1
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>1
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>2
[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>1
[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>2
[[[.,.],[.,[[.,.],[[.,.],.]]]],.]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>2
[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>2
[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>2
[[[.,.],[.,[[.,[.,[.,.]]],.]]],.]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>1
[[[.,.],[.,[[.,[[.,.],.]],.]]],.]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>1
[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>2
[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>1
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>1
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>1
[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>1
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>2
[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>1
[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>1
[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>2
[[[.,.],[[.,[.,.]],[[.,.],.]]],.]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>2
[[[.,.],[[[.,.],.],[.,[.,.]]]],.]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>1
[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>1
[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>2
[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>2
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>2
[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>2
[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>1
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>2
[[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>2
[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>3
[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>2
[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>2
[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>2
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>3
[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>2
[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>2
[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[[[.,.],[[[[.,.],[.,.]],.],.]],.]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>2
[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>1
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>1
[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>2
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>1
[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>1
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>1
[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>1
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>2
[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>1
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>2
[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>2
[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>2
[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>2
[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>1
[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>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
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>1
[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>1
[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>1
[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>2
[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>1
[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>2
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>2
[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>2
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>2
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>2
[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>2
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>2
[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>3
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>2
[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>1
[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>1
[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>1
[[[[.,[.,.]],.],[[.,[.,.]],.]],.]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>2
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>1
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>1
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>1
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>2
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>2
[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>2
[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>2
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>2
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>2
[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>2
[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>2
[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>2
[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>1
[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>1
[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>2
[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>2
[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>1
[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>1
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>2
[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>2
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>2
[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>3
[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>2
[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>2
[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>2
[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>2
[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>2
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>3
[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>2
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>2
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>2
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>2
[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>2
[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>2
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>1
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>2
[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>1
[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>1
[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>2
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>1
[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>1
[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>1
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>1
[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>2
[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>1
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>2
[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>2
[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>1
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>1
[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>1
[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>2
[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>1
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>1
[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>1
[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>2
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>2
[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>2
[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>1
[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>1
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>2
[[[[[.,.],[[.,.],.]],[.,.]],.],.]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>2
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>2
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>2
[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>1
[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>2
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>1
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>1
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>1
[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>1
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>1
[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>1
[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>1
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>2
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>1
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>1
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>1
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>0
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
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Description
The number of inner corners of the upper path of the parallelogram polyomino associated with the Dyck path.
Map
to Tamari-corresponding Dyck path
Description
Return the Dyck path associated with a binary tree in consistency with the Tamari order on Dyck words and binary trees.
The bijection is defined recursively as follows:
The bijection is defined recursively as follows:
- a leaf is associated with an empty Dyck path,
- a tree with children $l,r$ is associated with the Dyck word $T(l) 1 T(r) 0$ where $T(l)$ and $T(r)$ are the images of this bijection to $l$ and $r$.
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