Identifier
-
Mp00020:
Binary trees
—to Tamari-corresponding Dyck path⟶
Dyck paths
St001066: Dyck paths ⟶ ℤ
Values
=>
Cc0010;cc-rep-0
Cc0005;cc-rep
[.,.]=>[1,0]=>1
[.,[.,.]]=>[1,1,0,0]=>1
[[.,.],.]=>[1,0,1,0]=>1
[.,[.,[.,.]]]=>[1,1,1,0,0,0]=>1
[.,[[.,.],.]]=>[1,1,0,1,0,0]=>1
[[.,.],[.,.]]=>[1,0,1,1,0,0]=>1
[[.,[.,.]],.]=>[1,1,0,0,1,0]=>1
[[[.,.],.],.]=>[1,0,1,0,1,0]=>2
[.,[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0]=>1
[.,[.,[[.,.],.]]]=>[1,1,1,0,1,0,0,0]=>1
[.,[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,0]=>1
[.,[[.,[.,.]],.]]=>[1,1,1,0,0,1,0,0]=>1
[.,[[[.,.],.],.]]=>[1,1,0,1,0,1,0,0]=>2
[[.,.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0]=>1
[[.,.],[[.,.],.]]=>[1,0,1,1,0,1,0,0]=>2
[[.,[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0]=>1
[[[.,.],.],[.,.]]=>[1,0,1,0,1,1,0,0]=>2
[[.,[.,[.,.]]],.]=>[1,1,1,0,0,0,1,0]=>1
[[.,[[.,.],.]],.]=>[1,1,0,1,0,0,1,0]=>1
[[[.,.],[.,.]],.]=>[1,0,1,1,0,0,1,0]=>1
[[[.,[.,.]],.],.]=>[1,1,0,0,1,0,1,0]=>2
[[[[.,.],.],.],.]=>[1,0,1,0,1,0,1,0]=>3
[.,[.,[.,[.,[.,.]]]]]=>[1,1,1,1,1,0,0,0,0,0]=>1
[.,[.,[.,[[.,.],.]]]]=>[1,1,1,1,0,1,0,0,0,0]=>1
[.,[.,[[.,.],[.,.]]]]=>[1,1,1,0,1,1,0,0,0,0]=>1
[.,[.,[[.,[.,.]],.]]]=>[1,1,1,1,0,0,1,0,0,0]=>1
[.,[.,[[[.,.],.],.]]]=>[1,1,1,0,1,0,1,0,0,0]=>2
[.,[[.,.],[.,[.,.]]]]=>[1,1,0,1,1,1,0,0,0,0]=>1
[.,[[.,.],[[.,.],.]]]=>[1,1,0,1,1,0,1,0,0,0]=>2
[.,[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,0,0,0]=>1
[.,[[[.,.],.],[.,.]]]=>[1,1,0,1,0,1,1,0,0,0]=>2
[.,[[.,[.,[.,.]]],.]]=>[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]=>2
[.,[[[[.,.],.],.],.]]=>[1,1,0,1,0,1,0,1,0,0]=>3
[[.,.],[.,[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,0]=>1
[[.,.],[.,[[.,.],.]]]=>[1,0,1,1,1,0,1,0,0,0]=>2
[[.,.],[[.,.],[.,.]]]=>[1,0,1,1,0,1,1,0,0,0]=>2
[[.,.],[[.,[.,.]],.]]=>[1,0,1,1,1,0,0,1,0,0]=>1
[[.,.],[[[.,.],.],.]]=>[1,0,1,1,0,1,0,1,0,0]=>3
[[.,[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0]=>1
[[.,[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,1,0,0]=>2
[[[.,.],.],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0]=>2
[[[.,.],.],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0]=>3
[[.,[.,[.,.]]],[.,.]]=>[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]=>1
[[[.,[.,.]],.],[.,.]]=>[1,1,0,0,1,0,1,1,0,0]=>2
[[[[.,.],.],.],[.,.]]=>[1,0,1,0,1,0,1,1,0,0]=>3
[[.,[.,[.,[.,.]]]],.]=>[1,1,1,1,0,0,0,0,1,0]=>1
[[.,[.,[[.,.],.]]],.]=>[1,1,1,0,1,0,0,0,1,0]=>1
[[.,[[.,.],[.,.]]],.]=>[1,1,0,1,1,0,0,0,1,0]=>1
[[.,[[.,[.,.]],.]],.]=>[1,1,1,0,0,1,0,0,1,0]=>1
[[.,[[[.,.],.],.]],.]=>[1,1,0,1,0,1,0,0,1,0]=>2
[[[.,.],[.,[.,.]]],.]=>[1,0,1,1,1,0,0,0,1,0]=>1
[[[.,.],[[.,.],.]],.]=>[1,0,1,1,0,1,0,0,1,0]=>2
[[[.,[.,.]],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,0]=>1
[[[[.,.],.],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,0]=>2
[[[.,[.,[.,.]]],.],.]=>[1,1,1,0,0,0,1,0,1,0]=>2
[[[.,[[.,.],.]],.],.]=>[1,1,0,1,0,0,1,0,1,0]=>2
[[[[.,.],[.,.]],.],.]=>[1,0,1,1,0,0,1,0,1,0]=>2
[[[[.,[.,.]],.],.],.]=>[1,1,0,0,1,0,1,0,1,0]=>3
[[[[[.,.],.],.],.],.]=>[1,0,1,0,1,0,1,0,1,0]=>4
[.,[.,[.,[.,[.,[.,.]]]]]]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>1
[.,[.,[.,[.,[[.,.],.]]]]]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[.,[.,[.,[[.,.],[.,.]]]]]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[.,[.,[.,[[.,[.,.]],.]]]]=>[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]=>2
[.,[.,[[.,.],[.,[.,.]]]]]=>[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]=>2
[.,[.,[[.,[.,.]],[.,.]]]]=>[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]=>2
[.,[.,[[.,[.,[.,.]]],.]]]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[.,[.,[[.,[[.,.],.]],.]]]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[.,[.,[[[.,.],[.,.]],.]]]=>[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]=>2
[.,[.,[[[[.,.],.],.],.]]]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>3
[.,[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[.,[[.,.],[.,[[.,.],.]]]]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>2
[.,[[.,.],[[.,.],[.,.]]]]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>2
[.,[[.,.],[[.,[.,.]],.]]]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>1
[.,[[.,.],[[[.,.],.],.]]]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>3
[.,[[.,[.,.]],[.,[.,.]]]]=>[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]=>2
[.,[[[.,.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>2
[.,[[[.,.],.],[[.,.],.]]]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>3
[.,[[.,[.,[.,.]]],[.,.]]]=>[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]=>2
[.,[[[[.,.],.],.],[.,.]]]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>3
[.,[[.,[.,[.,[.,.]]]],.]]=>[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]=>1
[.,[[.,[[.,[.,.]],.]],.]]=>[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]=>2
[.,[[[.,.],[.,[.,.]]],.]]=>[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]=>2
[.,[[[.,[.,.]],[.,.]],.]]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>1
[.,[[[[.,.],.],[.,.]],.]]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>2
[.,[[[.,[.,[.,.]]],.],.]]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>2
[.,[[[.,[[.,.],.]],.],.]]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>2
[.,[[[[.,.],[.,.]],.],.]]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>2
[.,[[[[.,[.,.]],.],.],.]]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>3
[.,[[[[[.,.],.],.],.],.]]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>4
[[.,.],[.,[.,[.,[.,.]]]]]=>[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]=>2
[[.,.],[.,[[.,.],[.,.]]]]=>[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]=>3
[[.,.],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>2
[[.,.],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>3
[[.,.],[[.,[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>1
[[.,.],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>3
[[.,.],[[.,[.,[.,.]]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>1
[[.,.],[[.,[[.,.],.]],.]]=>[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]=>4
[[.,[.,.]],[.,[.,[.,.]]]]=>[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]=>2
[[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>2
[[.,[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>1
[[.,[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>3
[[[.,.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>2
[[[.,.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>3
[[[.,.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>3
[[[.,.],.],[[.,[.,.]],.]]=>[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]=>4
[[.,[.,[.,.]]],[.,[.,.]]]=>[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]=>2
[[.,[[.,.],.]],[.,[.,.]]]=>[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]=>2
[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>1
[[[.,.],[.,.]],[[.,.],.]]=>[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]=>2
[[[.,[.,.]],.],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>3
[[[[.,.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>3
[[[[.,.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>4
[[.,[.,[.,[.,.]]]],[.,.]]=>[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]=>1
[[.,[[[.,.],.],.]],[.,.]]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>2
[[[.,.],[.,[.,.]]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>1
[[[.,.],[[.,.],.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>2
[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>1
[[[[.,.],.],[.,.]],[.,.]]=>[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]=>2
[[[.,[[.,.],.]],.],[.,.]]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>2
[[[[.,.],[.,.]],.],[.,.]]=>[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]=>3
[[[[[.,.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>4
[[.,[.,[.,[.,[.,.]]]]],.]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[[.,[.,[.,[[.,.],.]]]],.]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>1
[[.,[.,[[.,.],[.,.]]]],.]=>[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]=>1
[[.,[.,[[[.,.],.],.]]],.]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>2
[[.,[[.,.],[.,[.,.]]]],.]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>1
[[.,[[.,.],[[.,.],.]]],.]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>2
[[.,[[.,[.,.]],[.,.]]],.]=>[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]=>2
[[.,[[.,[.,[.,.]]],.]],.]=>[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]=>2
[[.,[[[[.,.],.],.],.]],.]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>3
[[[.,.],[.,[.,[.,.]]]],.]=>[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]=>2
[[[.,.],[[.,.],[.,.]]],.]=>[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
[[[.,.],[[[.,.],.],.]],.]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>3
[[[.,[.,.]],[.,[.,.]]],.]=>[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]=>2
[[[[.,.],.],[.,[.,.]]],.]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>2
[[[[.,.],.],[[.,.],.]],.]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>3
[[[.,[.,[.,.]]],[.,.]],.]=>[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]=>1
[[[[.,[.,.]],.],[.,.]],.]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>2
[[[[[.,.],.],.],[.,.]],.]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>3
[[[.,[.,[.,[.,.]]]],.],.]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>2
[[[.,[.,[[.,.],.]]],.],.]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>2
[[[.,[[.,.],[.,.]]],.],.]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>2
[[[.,[[.,[.,.]],.]],.],.]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>2
[[[.,[[[.,.],.],.]],.],.]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>3
[[[[.,.],[.,[.,.]]],.],.]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>2
[[[[.,.],[[.,.],.]],.],.]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>3
[[[[.,[.,.]],[.,.]],.],.]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>2
[[[[[.,.],.],[.,.]],.],.]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>3
[[[[.,[.,[.,.]]],.],.],.]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>3
[[[[.,[[.,.],.]],.],.],.]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>3
[[[[[.,.],[.,.]],.],.],.]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>3
[[[[[.,[.,.]],.],.],.],.]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>4
[[[[[[.,.],.],.],.],.],.]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>5
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>1
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>1
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>1
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>1
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>2
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>1
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>2
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[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]=>2
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[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]=>2
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>3
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[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]=>2
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>2
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>1
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>3
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[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]=>2
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>2
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>3
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[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]=>1
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>2
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>3
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>1
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>1
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>1
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[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]=>2
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[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]=>2
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[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]=>2
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>2
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>2
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>2
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>3
[.,[.,[[[[[.,.],.],.],.],.]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>4
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>1
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>2
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>2
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>1
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>3
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>2
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>3
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[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]=>3
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>1
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>2
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>2
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>2
[.,[[.,.],[[[[.,.],.],.],.]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>4
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[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]=>2
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[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]=>3
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>2
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>3
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[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
[.,[[[.,.],.],[[[.,.],.],.]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>4
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[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]=>2
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[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]=>2
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[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]=>2
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>2
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>3
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>3
[.,[[[[.,.],.],.],[[.,.],.]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>4
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[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]=>1
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[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]=>2
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[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]=>2
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>1
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>2
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>2
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>2
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>2
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>3
[.,[[[[[.,.],.],.],.],[.,.]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>4
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[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]=>1
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>2
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>1
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[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]=>1
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[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]=>1
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>2
[.,[[.,[[[[.,.],.],.],.]],.]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>3
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[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]=>2
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>2
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>1
[.,[[[.,.],[[[.,.],.],.]],.]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>3
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>1
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[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]=>2
[.,[[[[.,.],.],[[.,.],.]],.]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>3
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>1
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>1
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>1
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[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]=>3
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>2
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>2
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[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]=>2
[.,[[[.,[[[.,.],.],.]],.],.]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>3
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>2
[.,[[[[.,.],[[.,.],.]],.],.]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>3
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[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]=>3
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>3
[.,[[[[.,[[.,.],.]],.],.],.]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>3
[.,[[[[[.,.],[.,.]],.],.],.]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>3
[.,[[[[[.,[.,.]],.],.],.],.]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>4
[.,[[[[[[.,.],.],.],.],.],.]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>5
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[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]=>2
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[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
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>3
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[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]=>3
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>1
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>3
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[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]=>2
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[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]=>2
[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>4
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>2
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>3
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[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
[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>4
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>1
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[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]=>3
[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>4
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>1
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[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]=>4
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>1
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[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]=>2
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>1
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>3
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[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]=>3
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>1
[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>3
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[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]=>3
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>3
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>3
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>5
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[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]=>2
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>2
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>1
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>3
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>2
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>3
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>1
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>3
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>1
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[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]=>4
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>2
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>3
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>3
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>2
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>4
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>3
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>4
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[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]=>4
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[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]=>3
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>3
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>3
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>5
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[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]=>2
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>2
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>1
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>3
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[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]=>2
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>2
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>1
[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>3
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>1
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[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]=>1
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>3
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>2
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>3
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[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
[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>4
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>3
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>4
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>4
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>3
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>5
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[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]=>2
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[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]=>2
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[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]=>2
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>1
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[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]=>2
[[.,[[[.,.],.],.]],[[.,.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>3
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>1
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[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]=>3
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>1
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[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]=>3
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>2
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>3
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>2
[[[.,[[.,.],.]],.],[[.,.],.]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>3
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[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]=>3
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>3
[[[[.,[.,.]],.],.],[[.,.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>4
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>4
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>5
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[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]=>1
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[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]=>2
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[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]=>2
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>1
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>2
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>1
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>1
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>1
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[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]=>3
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>1
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[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]=>1
[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>3
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>1
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[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]=>3
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>1
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>1
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>1
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[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]=>3
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>2
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>2
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>2
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[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]=>3
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[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]=>3
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[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]=>3
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>3
[[[[.,[[.,.],.]],.],.],[.,.]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>3
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>3
[[[[[.,[.,.]],.],.],.],[.,.]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>4
[[[[[[.,.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>5
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>1
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>1
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>1
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[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]=>2
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[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]=>2
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[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]=>2
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>1
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>1
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[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]=>2
[[.,[.,[[[[.,.],.],.],.]]],.]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>3
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>1
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>2
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>2
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>1
[[.,[[.,.],[[[.,.],.],.]]],.]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>3
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[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]=>2
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>2
[[.,[[[.,.],.],[[.,.],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>3
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[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]=>2
[[.,[[[[.,.],.],.],[.,.]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>3
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[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]=>1
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[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]=>2
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[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]=>2
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>1
[[.,[[[[.,.],.],[.,.]],.]],.]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>2
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>2
[[.,[[[.,[[.,.],.]],.],.]],.]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[[.,[[[[.,.],[.,.]],.],.]],.]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>2
[[.,[[[[.,[.,.]],.],.],.]],.]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>3
[[.,[[[[[.,.],.],.],.],.]],.]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>4
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[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]=>2
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[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]=>3
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>2
[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>3
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>1
[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>3
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>1
[[[.,.],[[.,[[.,.],.]],.]],.]=>[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]=>4
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[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]=>2
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>2
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>1
[[[.,[.,.]],[[[.,.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>3
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>2
[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>3
[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>3
[[[[.,.],.],[[.,[.,.]],.]],.]=>[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]=>4
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[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]=>2
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[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]=>2
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>1
[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>2
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>2
[[[[.,[.,.]],.],[[.,.],.]],.]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>3
[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>3
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>4
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[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]=>1
[[[.,[[[.,.],.],.]],[.,.]],.]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>2
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>1
[[[[.,.],[[.,.],.]],[.,.]],.]=>[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]=>1
[[[[[.,.],.],[.,.]],[.,.]],.]=>[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]=>2
[[[[.,[[.,.],.]],.],[.,.]],.]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>2
[[[[[.,.],[.,.]],.],[.,.]],.]=>[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]=>3
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>4
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>2
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>2
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>2
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>2
[[[.,[.,[[[.,.],.],.]]],.],.]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>3
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>2
[[[.,[[.,.],[[.,.],.]]],.],.]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>3
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>2
[[[.,[[[.,.],.],[.,.]]],.],.]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>3
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>2
[[[.,[[.,[[.,.],.]],.]],.],.]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[[[.,[[[.,.],[.,.]],.]],.],.]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>2
[[[.,[[[.,[.,.]],.],.]],.],.]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>3
[[[.,[[[[.,.],.],.],.]],.],.]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>4
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>2
[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>3
[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>3
[[[[.,.],[[.,[.,.]],.]],.],.]=>[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]=>4
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>2
[[[[.,[.,.]],[[.,.],.]],.],.]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>3
[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>3
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>4
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>2
[[[[.,[[.,.],.]],[.,.]],.],.]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>2
[[[[[.,.],[.,.]],[.,.]],.],.]=>[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]=>3
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>4
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>3
[[[[.,[.,[[.,.],.]]],.],.],.]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>3
[[[[.,[[.,.],[.,.]]],.],.],.]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>3
[[[[.,[[.,[.,.]],.]],.],.],.]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>3
[[[[.,[[[.,.],.],.]],.],.],.]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>4
[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>3
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>4
[[[[[.,[.,.]],[.,.]],.],.],.]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>3
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>4
[[[[[.,[.,[.,.]]],.],.],.],.]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>4
[[[[[.,[[.,.],.]],.],.],.],.]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>4
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>4
[[[[[[.,[.,.]],.],.],.],.],.]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>5
[[[[[[[.,.],.],.],.],.],.],.]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>6
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Description
The number of simple reflexive modules in the corresponding Nakayama algebra.
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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