Identifier
- St000201: Binary trees ⟶ ℤ (values match St000196The number of occurrences of the contiguous pattern [[.,.],[.,.)
Values
=>
Cc0010;cc-rep
[.,.]=>1
[.,[.,.]]=>1
[[.,.],.]=>1
[.,[.,[.,.]]]=>1
[.,[[.,.],.]]=>1
[[.,.],[.,.]]=>2
[[.,[.,.]],.]=>1
[[[.,.],.],.]=>1
[.,[.,[.,[.,.]]]]=>1
[.,[.,[[.,.],.]]]=>1
[.,[[.,.],[.,.]]]=>2
[.,[[.,[.,.]],.]]=>1
[.,[[[.,.],.],.]]=>1
[[.,.],[.,[.,.]]]=>2
[[.,.],[[.,.],.]]=>2
[[.,[.,.]],[.,.]]=>2
[[[.,.],.],[.,.]]=>2
[[.,[.,[.,.]]],.]=>1
[[.,[[.,.],.]],.]=>1
[[[.,.],[.,.]],.]=>2
[[[.,[.,.]],.],.]=>1
[[[[.,.],.],.],.]=>1
[.,[.,[.,[.,[.,.]]]]]=>1
[.,[.,[.,[[.,.],.]]]]=>1
[.,[.,[[.,.],[.,.]]]]=>2
[.,[.,[[.,[.,.]],.]]]=>1
[.,[.,[[[.,.],.],.]]]=>1
[.,[[.,.],[.,[.,.]]]]=>2
[.,[[.,.],[[.,.],.]]]=>2
[.,[[.,[.,.]],[.,.]]]=>2
[.,[[[.,.],.],[.,.]]]=>2
[.,[[.,[.,[.,.]]],.]]=>1
[.,[[.,[[.,.],.]],.]]=>1
[.,[[[.,.],[.,.]],.]]=>2
[.,[[[.,[.,.]],.],.]]=>1
[.,[[[[.,.],.],.],.]]=>1
[[.,.],[.,[.,[.,.]]]]=>2
[[.,.],[.,[[.,.],.]]]=>2
[[.,.],[[.,.],[.,.]]]=>3
[[.,.],[[.,[.,.]],.]]=>2
[[.,.],[[[.,.],.],.]]=>2
[[.,[.,.]],[.,[.,.]]]=>2
[[.,[.,.]],[[.,.],.]]=>2
[[[.,.],.],[.,[.,.]]]=>2
[[[.,.],.],[[.,.],.]]=>2
[[.,[.,[.,.]]],[.,.]]=>2
[[.,[[.,.],.]],[.,.]]=>2
[[[.,.],[.,.]],[.,.]]=>3
[[[.,[.,.]],.],[.,.]]=>2
[[[[.,.],.],.],[.,.]]=>2
[[.,[.,[.,[.,.]]]],.]=>1
[[.,[.,[[.,.],.]]],.]=>1
[[.,[[.,.],[.,.]]],.]=>2
[[.,[[.,[.,.]],.]],.]=>1
[[.,[[[.,.],.],.]],.]=>1
[[[.,.],[.,[.,.]]],.]=>2
[[[.,.],[[.,.],.]],.]=>2
[[[.,[.,.]],[.,.]],.]=>2
[[[[.,.],.],[.,.]],.]=>2
[[[.,[.,[.,.]]],.],.]=>1
[[[.,[[.,.],.]],.],.]=>1
[[[[.,.],[.,.]],.],.]=>2
[[[[.,[.,.]],.],.],.]=>1
[[[[[.,.],.],.],.],.]=>1
[.,[.,[.,[.,[.,[.,.]]]]]]=>1
[.,[.,[.,[.,[[.,.],.]]]]]=>1
[.,[.,[.,[[.,.],[.,.]]]]]=>2
[.,[.,[.,[[.,[.,.]],.]]]]=>1
[.,[.,[.,[[[.,.],.],.]]]]=>1
[.,[.,[[.,.],[.,[.,.]]]]]=>2
[.,[.,[[.,.],[[.,.],.]]]]=>2
[.,[.,[[.,[.,.]],[.,.]]]]=>2
[.,[.,[[[.,.],.],[.,.]]]]=>2
[.,[.,[[.,[.,[.,.]]],.]]]=>1
[.,[.,[[.,[[.,.],.]],.]]]=>1
[.,[.,[[[.,.],[.,.]],.]]]=>2
[.,[.,[[[.,[.,.]],.],.]]]=>1
[.,[.,[[[[.,.],.],.],.]]]=>1
[.,[[.,.],[.,[.,[.,.]]]]]=>2
[.,[[.,.],[.,[[.,.],.]]]]=>2
[.,[[.,.],[[.,.],[.,.]]]]=>3
[.,[[.,.],[[.,[.,.]],.]]]=>2
[.,[[.,.],[[[.,.],.],.]]]=>2
[.,[[.,[.,.]],[.,[.,.]]]]=>2
[.,[[.,[.,.]],[[.,.],.]]]=>2
[.,[[[.,.],.],[.,[.,.]]]]=>2
[.,[[[.,.],.],[[.,.],.]]]=>2
[.,[[.,[.,[.,.]]],[.,.]]]=>2
[.,[[.,[[.,.],.]],[.,.]]]=>2
[.,[[[.,.],[.,.]],[.,.]]]=>3
[.,[[[.,[.,.]],.],[.,.]]]=>2
[.,[[[[.,.],.],.],[.,.]]]=>2
[.,[[.,[.,[.,[.,.]]]],.]]=>1
[.,[[.,[.,[[.,.],.]]],.]]=>1
[.,[[.,[[.,.],[.,.]]],.]]=>2
[.,[[.,[[.,[.,.]],.]],.]]=>1
[.,[[.,[[[.,.],.],.]],.]]=>1
[.,[[[.,.],[.,[.,.]]],.]]=>2
[.,[[[.,.],[[.,.],.]],.]]=>2
[.,[[[.,[.,.]],[.,.]],.]]=>2
[.,[[[[.,.],.],[.,.]],.]]=>2
[.,[[[.,[.,[.,.]]],.],.]]=>1
[.,[[[.,[[.,.],.]],.],.]]=>1
[.,[[[[.,.],[.,.]],.],.]]=>2
[.,[[[[.,[.,.]],.],.],.]]=>1
[.,[[[[[.,.],.],.],.],.]]=>1
[[.,.],[.,[.,[.,[.,.]]]]]=>2
[[.,.],[.,[.,[[.,.],.]]]]=>2
[[.,.],[.,[[.,.],[.,.]]]]=>3
[[.,.],[.,[[.,[.,.]],.]]]=>2
[[.,.],[.,[[[.,.],.],.]]]=>2
[[.,.],[[.,.],[.,[.,.]]]]=>3
[[.,.],[[.,.],[[.,.],.]]]=>3
[[.,.],[[.,[.,.]],[.,.]]]=>3
[[.,.],[[[.,.],.],[.,.]]]=>3
[[.,.],[[.,[.,[.,.]]],.]]=>2
[[.,.],[[.,[[.,.],.]],.]]=>2
[[.,.],[[[.,.],[.,.]],.]]=>3
[[.,.],[[[.,[.,.]],.],.]]=>2
[[.,.],[[[[.,.],.],.],.]]=>2
[[.,[.,.]],[.,[.,[.,.]]]]=>2
[[.,[.,.]],[.,[[.,.],.]]]=>2
[[.,[.,.]],[[.,.],[.,.]]]=>3
[[.,[.,.]],[[.,[.,.]],.]]=>2
[[.,[.,.]],[[[.,.],.],.]]=>2
[[[.,.],.],[.,[.,[.,.]]]]=>2
[[[.,.],.],[.,[[.,.],.]]]=>2
[[[.,.],.],[[.,.],[.,.]]]=>3
[[[.,.],.],[[.,[.,.]],.]]=>2
[[[.,.],.],[[[.,.],.],.]]=>2
[[.,[.,[.,.]]],[.,[.,.]]]=>2
[[.,[.,[.,.]]],[[.,.],.]]=>2
[[.,[[.,.],.]],[.,[.,.]]]=>2
[[.,[[.,.],.]],[[.,.],.]]=>2
[[[.,.],[.,.]],[.,[.,.]]]=>3
[[[.,.],[.,.]],[[.,.],.]]=>3
[[[.,[.,.]],.],[.,[.,.]]]=>2
[[[.,[.,.]],.],[[.,.],.]]=>2
[[[[.,.],.],.],[.,[.,.]]]=>2
[[[[.,.],.],.],[[.,.],.]]=>2
[[.,[.,[.,[.,.]]]],[.,.]]=>2
[[.,[.,[[.,.],.]]],[.,.]]=>2
[[.,[[.,.],[.,.]]],[.,.]]=>3
[[.,[[.,[.,.]],.]],[.,.]]=>2
[[.,[[[.,.],.],.]],[.,.]]=>2
[[[.,.],[.,[.,.]]],[.,.]]=>3
[[[.,.],[[.,.],.]],[.,.]]=>3
[[[.,[.,.]],[.,.]],[.,.]]=>3
[[[[.,.],.],[.,.]],[.,.]]=>3
[[[.,[.,[.,.]]],.],[.,.]]=>2
[[[.,[[.,.],.]],.],[.,.]]=>2
[[[[.,.],[.,.]],.],[.,.]]=>3
[[[[.,[.,.]],.],.],[.,.]]=>2
[[[[[.,.],.],.],.],[.,.]]=>2
[[.,[.,[.,[.,[.,.]]]]],.]=>1
[[.,[.,[.,[[.,.],.]]]],.]=>1
[[.,[.,[[.,.],[.,.]]]],.]=>2
[[.,[.,[[.,[.,.]],.]]],.]=>1
[[.,[.,[[[.,.],.],.]]],.]=>1
[[.,[[.,.],[.,[.,.]]]],.]=>2
[[.,[[.,.],[[.,.],.]]],.]=>2
[[.,[[.,[.,.]],[.,.]]],.]=>2
[[.,[[[.,.],.],[.,.]]],.]=>2
[[.,[[.,[.,[.,.]]],.]],.]=>1
[[.,[[.,[[.,.],.]],.]],.]=>1
[[.,[[[.,.],[.,.]],.]],.]=>2
[[.,[[[.,[.,.]],.],.]],.]=>1
[[.,[[[[.,.],.],.],.]],.]=>1
[[[.,.],[.,[.,[.,.]]]],.]=>2
[[[.,.],[.,[[.,.],.]]],.]=>2
[[[.,.],[[.,.],[.,.]]],.]=>3
[[[.,.],[[.,[.,.]],.]],.]=>2
[[[.,.],[[[.,.],.],.]],.]=>2
[[[.,[.,.]],[.,[.,.]]],.]=>2
[[[.,[.,.]],[[.,.],.]],.]=>2
[[[[.,.],.],[.,[.,.]]],.]=>2
[[[[.,.],.],[[.,.],.]],.]=>2
[[[.,[.,[.,.]]],[.,.]],.]=>2
[[[.,[[.,.],.]],[.,.]],.]=>2
[[[[.,.],[.,.]],[.,.]],.]=>3
[[[[.,[.,.]],.],[.,.]],.]=>2
[[[[[.,.],.],.],[.,.]],.]=>2
[[[.,[.,[.,[.,.]]]],.],.]=>1
[[[.,[.,[[.,.],.]]],.],.]=>1
[[[.,[[.,.],[.,.]]],.],.]=>2
[[[.,[[.,[.,.]],.]],.],.]=>1
[[[.,[[[.,.],.],.]],.],.]=>1
[[[[.,.],[.,[.,.]]],.],.]=>2
[[[[.,.],[[.,.],.]],.],.]=>2
[[[[.,[.,.]],[.,.]],.],.]=>2
[[[[[.,.],.],[.,.]],.],.]=>2
[[[[.,[.,[.,.]]],.],.],.]=>1
[[[[.,[[.,.],.]],.],.],.]=>1
[[[[[.,.],[.,.]],.],.],.]=>2
[[[[[.,[.,.]],.],.],.],.]=>1
[[[[[[.,.],.],.],.],.],.]=>1
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>1
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>1
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>2
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>1
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>1
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>2
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>2
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>2
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>2
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>1
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>1
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>2
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>1
[.,[.,[.,[[[[.,.],.],.],.]]]]=>1
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>2
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>2
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>3
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>2
[.,[.,[[.,.],[[[.,.],.],.]]]]=>2
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>2
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>2
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>2
[.,[.,[[[.,.],.],[[.,.],.]]]]=>2
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>2
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>2
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>3
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>2
[.,[.,[[[[.,.],.],.],[.,.]]]]=>2
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>1
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>1
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>2
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>1
[.,[.,[[.,[[[.,.],.],.]],.]]]=>1
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>2
[.,[.,[[[.,.],[[.,.],.]],.]]]=>2
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>2
[.,[.,[[[[.,.],.],[.,.]],.]]]=>2
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>1
[.,[.,[[[.,[[.,.],.]],.],.]]]=>1
[.,[.,[[[[.,.],[.,.]],.],.]]]=>2
[.,[.,[[[[.,[.,.]],.],.],.]]]=>1
[.,[.,[[[[[.,.],.],.],.],.]]]=>1
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>2
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>2
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>3
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>2
[.,[[.,.],[.,[[[.,.],.],.]]]]=>2
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>3
[.,[[.,.],[[.,.],[[.,.],.]]]]=>3
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>3
[.,[[.,.],[[[.,.],.],[.,.]]]]=>3
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>2
[.,[[.,.],[[.,[[.,.],.]],.]]]=>2
[.,[[.,.],[[[.,.],[.,.]],.]]]=>3
[.,[[.,.],[[[.,[.,.]],.],.]]]=>2
[.,[[.,.],[[[[.,.],.],.],.]]]=>2
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>2
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>2
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>3
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>2
[.,[[.,[.,.]],[[[.,.],.],.]]]=>2
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>2
[.,[[[.,.],.],[.,[[.,.],.]]]]=>2
[.,[[[.,.],.],[[.,.],[.,.]]]]=>3
[.,[[[.,.],.],[[.,[.,.]],.]]]=>2
[.,[[[.,.],.],[[[.,.],.],.]]]=>2
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>2
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>2
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>2
[.,[[.,[[.,.],.]],[[.,.],.]]]=>2
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>3
[.,[[[.,.],[.,.]],[[.,.],.]]]=>3
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>2
[.,[[[.,[.,.]],.],[[.,.],.]]]=>2
[.,[[[[.,.],.],.],[.,[.,.]]]]=>2
[.,[[[[.,.],.],.],[[.,.],.]]]=>2
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>2
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>2
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>3
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>2
[.,[[.,[[[.,.],.],.]],[.,.]]]=>2
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>3
[.,[[[.,.],[[.,.],.]],[.,.]]]=>3
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>3
[.,[[[[.,.],.],[.,.]],[.,.]]]=>3
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>2
[.,[[[.,[[.,.],.]],.],[.,.]]]=>2
[.,[[[[.,.],[.,.]],.],[.,.]]]=>3
[.,[[[[.,[.,.]],.],.],[.,.]]]=>2
[.,[[[[[.,.],.],.],.],[.,.]]]=>2
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>1
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>1
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>2
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>1
[.,[[.,[.,[[[.,.],.],.]]],.]]=>1
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>2
[.,[[.,[[.,.],[[.,.],.]]],.]]=>2
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>2
[.,[[.,[[[.,.],.],[.,.]]],.]]=>2
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>1
[.,[[.,[[.,[[.,.],.]],.]],.]]=>1
[.,[[.,[[[.,.],[.,.]],.]],.]]=>2
[.,[[.,[[[.,[.,.]],.],.]],.]]=>1
[.,[[.,[[[[.,.],.],.],.]],.]]=>1
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>2
[.,[[[.,.],[.,[[.,.],.]]],.]]=>2
[.,[[[.,.],[[.,.],[.,.]]],.]]=>3
[.,[[[.,.],[[.,[.,.]],.]],.]]=>2
[.,[[[.,.],[[[.,.],.],.]],.]]=>2
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>2
[.,[[[.,[.,.]],[[.,.],.]],.]]=>2
[.,[[[[.,.],.],[.,[.,.]]],.]]=>2
[.,[[[[.,.],.],[[.,.],.]],.]]=>2
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>2
[.,[[[.,[[.,.],.]],[.,.]],.]]=>2
[.,[[[[.,.],[.,.]],[.,.]],.]]=>3
[.,[[[[.,[.,.]],.],[.,.]],.]]=>2
[.,[[[[[.,.],.],.],[.,.]],.]]=>2
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>1
[.,[[[.,[.,[[.,.],.]]],.],.]]=>1
[.,[[[.,[[.,.],[.,.]]],.],.]]=>2
[.,[[[.,[[.,[.,.]],.]],.],.]]=>1
[.,[[[.,[[[.,.],.],.]],.],.]]=>1
[.,[[[[.,.],[.,[.,.]]],.],.]]=>2
[.,[[[[.,.],[[.,.],.]],.],.]]=>2
[.,[[[[.,[.,.]],[.,.]],.],.]]=>2
[.,[[[[[.,.],.],[.,.]],.],.]]=>2
[.,[[[[.,[.,[.,.]]],.],.],.]]=>1
[.,[[[[.,[[.,.],.]],.],.],.]]=>1
[.,[[[[[.,.],[.,.]],.],.],.]]=>2
[.,[[[[[.,[.,.]],.],.],.],.]]=>1
[.,[[[[[[.,.],.],.],.],.],.]]=>1
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>2
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>2
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>3
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>2
[[.,.],[.,[.,[[[.,.],.],.]]]]=>2
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>3
[[.,.],[.,[[.,.],[[.,.],.]]]]=>3
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>3
[[.,.],[.,[[[.,.],.],[.,.]]]]=>3
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>2
[[.,.],[.,[[.,[[.,.],.]],.]]]=>2
[[.,.],[.,[[[.,.],[.,.]],.]]]=>3
[[.,.],[.,[[[.,[.,.]],.],.]]]=>2
[[.,.],[.,[[[[.,.],.],.],.]]]=>2
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>3
[[.,.],[[.,.],[.,[[.,.],.]]]]=>3
[[.,.],[[.,.],[[.,.],[.,.]]]]=>4
[[.,.],[[.,.],[[.,[.,.]],.]]]=>3
[[.,.],[[.,.],[[[.,.],.],.]]]=>3
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>3
[[.,.],[[.,[.,.]],[[.,.],.]]]=>3
[[.,.],[[[.,.],.],[.,[.,.]]]]=>3
[[.,.],[[[.,.],.],[[.,.],.]]]=>3
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>3
[[.,.],[[.,[[.,.],.]],[.,.]]]=>3
[[.,.],[[[.,.],[.,.]],[.,.]]]=>4
[[.,.],[[[.,[.,.]],.],[.,.]]]=>3
[[.,.],[[[[.,.],.],.],[.,.]]]=>3
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>2
[[.,.],[[.,[.,[[.,.],.]]],.]]=>2
[[.,.],[[.,[[.,.],[.,.]]],.]]=>3
[[.,.],[[.,[[.,[.,.]],.]],.]]=>2
[[.,.],[[.,[[[.,.],.],.]],.]]=>2
[[.,.],[[[.,.],[.,[.,.]]],.]]=>3
[[.,.],[[[.,.],[[.,.],.]],.]]=>3
[[.,.],[[[.,[.,.]],[.,.]],.]]=>3
[[.,.],[[[[.,.],.],[.,.]],.]]=>3
[[.,.],[[[.,[.,[.,.]]],.],.]]=>2
[[.,.],[[[.,[[.,.],.]],.],.]]=>2
[[.,.],[[[[.,.],[.,.]],.],.]]=>3
[[.,.],[[[[.,[.,.]],.],.],.]]=>2
[[.,.],[[[[[.,.],.],.],.],.]]=>2
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>2
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>2
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>3
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>2
[[.,[.,.]],[.,[[[.,.],.],.]]]=>2
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>3
[[.,[.,.]],[[.,.],[[.,.],.]]]=>3
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>3
[[.,[.,.]],[[[.,.],.],[.,.]]]=>3
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>2
[[.,[.,.]],[[.,[[.,.],.]],.]]=>2
[[.,[.,.]],[[[.,.],[.,.]],.]]=>3
[[.,[.,.]],[[[.,[.,.]],.],.]]=>2
[[.,[.,.]],[[[[.,.],.],.],.]]=>2
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>2
[[[.,.],.],[.,[.,[[.,.],.]]]]=>2
[[[.,.],.],[.,[[.,.],[.,.]]]]=>3
[[[.,.],.],[.,[[.,[.,.]],.]]]=>2
[[[.,.],.],[.,[[[.,.],.],.]]]=>2
[[[.,.],.],[[.,.],[.,[.,.]]]]=>3
[[[.,.],.],[[.,.],[[.,.],.]]]=>3
[[[.,.],.],[[.,[.,.]],[.,.]]]=>3
[[[.,.],.],[[[.,.],.],[.,.]]]=>3
[[[.,.],.],[[.,[.,[.,.]]],.]]=>2
[[[.,.],.],[[.,[[.,.],.]],.]]=>2
[[[.,.],.],[[[.,.],[.,.]],.]]=>3
[[[.,.],.],[[[.,[.,.]],.],.]]=>2
[[[.,.],.],[[[[.,.],.],.],.]]=>2
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>2
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>2
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>3
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>2
[[.,[.,[.,.]]],[[[.,.],.],.]]=>2
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>2
[[.,[[.,.],.]],[.,[[.,.],.]]]=>2
[[.,[[.,.],.]],[[.,.],[.,.]]]=>3
[[.,[[.,.],.]],[[.,[.,.]],.]]=>2
[[.,[[.,.],.]],[[[.,.],.],.]]=>2
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>3
[[[.,.],[.,.]],[.,[[.,.],.]]]=>3
[[[.,.],[.,.]],[[.,.],[.,.]]]=>4
[[[.,.],[.,.]],[[.,[.,.]],.]]=>3
[[[.,.],[.,.]],[[[.,.],.],.]]=>3
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>2
[[[.,[.,.]],.],[.,[[.,.],.]]]=>2
[[[.,[.,.]],.],[[.,.],[.,.]]]=>3
[[[.,[.,.]],.],[[.,[.,.]],.]]=>2
[[[.,[.,.]],.],[[[.,.],.],.]]=>2
[[[[.,.],.],.],[.,[.,[.,.]]]]=>2
[[[[.,.],.],.],[.,[[.,.],.]]]=>2
[[[[.,.],.],.],[[.,.],[.,.]]]=>3
[[[[.,.],.],.],[[.,[.,.]],.]]=>2
[[[[.,.],.],.],[[[.,.],.],.]]=>2
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>2
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>2
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>2
[[.,[.,[[.,.],.]]],[[.,.],.]]=>2
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>3
[[.,[[.,.],[.,.]]],[[.,.],.]]=>3
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>2
[[.,[[.,[.,.]],.]],[[.,.],.]]=>2
[[.,[[[.,.],.],.]],[.,[.,.]]]=>2
[[.,[[[.,.],.],.]],[[.,.],.]]=>2
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>3
[[[.,.],[.,[.,.]]],[[.,.],.]]=>3
[[[.,.],[[.,.],.]],[.,[.,.]]]=>3
[[[.,.],[[.,.],.]],[[.,.],.]]=>3
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>3
[[[.,[.,.]],[.,.]],[[.,.],.]]=>3
[[[[.,.],.],[.,.]],[.,[.,.]]]=>3
[[[[.,.],.],[.,.]],[[.,.],.]]=>3
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>2
[[[.,[.,[.,.]]],.],[[.,.],.]]=>2
[[[.,[[.,.],.]],.],[.,[.,.]]]=>2
[[[.,[[.,.],.]],.],[[.,.],.]]=>2
[[[[.,.],[.,.]],.],[.,[.,.]]]=>3
[[[[.,.],[.,.]],.],[[.,.],.]]=>3
[[[[.,[.,.]],.],.],[.,[.,.]]]=>2
[[[[.,[.,.]],.],.],[[.,.],.]]=>2
[[[[[.,.],.],.],.],[.,[.,.]]]=>2
[[[[[.,.],.],.],.],[[.,.],.]]=>2
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>2
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>2
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>3
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>2
[[.,[.,[[[.,.],.],.]]],[.,.]]=>2
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>3
[[.,[[.,.],[[.,.],.]]],[.,.]]=>3
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>3
[[.,[[[.,.],.],[.,.]]],[.,.]]=>3
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>2
[[.,[[.,[[.,.],.]],.]],[.,.]]=>2
[[.,[[[.,.],[.,.]],.]],[.,.]]=>3
[[.,[[[.,[.,.]],.],.]],[.,.]]=>2
[[.,[[[[.,.],.],.],.]],[.,.]]=>2
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>3
[[[.,.],[.,[[.,.],.]]],[.,.]]=>3
[[[.,.],[[.,.],[.,.]]],[.,.]]=>4
[[[.,.],[[.,[.,.]],.]],[.,.]]=>3
[[[.,.],[[[.,.],.],.]],[.,.]]=>3
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>3
[[[.,[.,.]],[[.,.],.]],[.,.]]=>3
[[[[.,.],.],[.,[.,.]]],[.,.]]=>3
[[[[.,.],.],[[.,.],.]],[.,.]]=>3
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>3
[[[.,[[.,.],.]],[.,.]],[.,.]]=>3
[[[[.,.],[.,.]],[.,.]],[.,.]]=>4
[[[[.,[.,.]],.],[.,.]],[.,.]]=>3
[[[[[.,.],.],.],[.,.]],[.,.]]=>3
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>2
[[[.,[.,[[.,.],.]]],.],[.,.]]=>2
[[[.,[[.,.],[.,.]]],.],[.,.]]=>3
[[[.,[[.,[.,.]],.]],.],[.,.]]=>2
[[[.,[[[.,.],.],.]],.],[.,.]]=>2
[[[[.,.],[.,[.,.]]],.],[.,.]]=>3
[[[[.,.],[[.,.],.]],.],[.,.]]=>3
[[[[.,[.,.]],[.,.]],.],[.,.]]=>3
[[[[[.,.],.],[.,.]],.],[.,.]]=>3
[[[[.,[.,[.,.]]],.],.],[.,.]]=>2
[[[[.,[[.,.],.]],.],.],[.,.]]=>2
[[[[[.,.],[.,.]],.],.],[.,.]]=>3
[[[[[.,[.,.]],.],.],.],[.,.]]=>2
[[[[[[.,.],.],.],.],.],[.,.]]=>2
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>1
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>1
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>2
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>1
[[.,[.,[.,[[[.,.],.],.]]]],.]=>1
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>2
[[.,[.,[[.,.],[[.,.],.]]]],.]=>2
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>2
[[.,[.,[[[.,.],.],[.,.]]]],.]=>2
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>1
[[.,[.,[[.,[[.,.],.]],.]]],.]=>1
[[.,[.,[[[.,.],[.,.]],.]]],.]=>2
[[.,[.,[[[.,[.,.]],.],.]]],.]=>1
[[.,[.,[[[[.,.],.],.],.]]],.]=>1
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>2
[[.,[[.,.],[.,[[.,.],.]]]],.]=>2
[[.,[[.,.],[[.,.],[.,.]]]],.]=>3
[[.,[[.,.],[[.,[.,.]],.]]],.]=>2
[[.,[[.,.],[[[.,.],.],.]]],.]=>2
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>2
[[.,[[.,[.,.]],[[.,.],.]]],.]=>2
[[.,[[[.,.],.],[.,[.,.]]]],.]=>2
[[.,[[[.,.],.],[[.,.],.]]],.]=>2
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>2
[[.,[[.,[[.,.],.]],[.,.]]],.]=>2
[[.,[[[.,.],[.,.]],[.,.]]],.]=>3
[[.,[[[.,[.,.]],.],[.,.]]],.]=>2
[[.,[[[[.,.],.],.],[.,.]]],.]=>2
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>1
[[.,[[.,[.,[[.,.],.]]],.]],.]=>1
[[.,[[.,[[.,.],[.,.]]],.]],.]=>2
[[.,[[.,[[.,[.,.]],.]],.]],.]=>1
[[.,[[.,[[[.,.],.],.]],.]],.]=>1
[[.,[[[.,.],[.,[.,.]]],.]],.]=>2
[[.,[[[.,.],[[.,.],.]],.]],.]=>2
[[.,[[[.,[.,.]],[.,.]],.]],.]=>2
[[.,[[[[.,.],.],[.,.]],.]],.]=>2
[[.,[[[.,[.,[.,.]]],.],.]],.]=>1
[[.,[[[.,[[.,.],.]],.],.]],.]=>1
[[.,[[[[.,.],[.,.]],.],.]],.]=>2
[[.,[[[[.,[.,.]],.],.],.]],.]=>1
[[.,[[[[[.,.],.],.],.],.]],.]=>1
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>2
[[[.,.],[.,[.,[[.,.],.]]]],.]=>2
[[[.,.],[.,[[.,.],[.,.]]]],.]=>3
[[[.,.],[.,[[.,[.,.]],.]]],.]=>2
[[[.,.],[.,[[[.,.],.],.]]],.]=>2
[[[.,.],[[.,.],[.,[.,.]]]],.]=>3
[[[.,.],[[.,.],[[.,.],.]]],.]=>3
[[[.,.],[[.,[.,.]],[.,.]]],.]=>3
[[[.,.],[[[.,.],.],[.,.]]],.]=>3
[[[.,.],[[.,[.,[.,.]]],.]],.]=>2
[[[.,.],[[.,[[.,.],.]],.]],.]=>2
[[[.,.],[[[.,.],[.,.]],.]],.]=>3
[[[.,.],[[[.,[.,.]],.],.]],.]=>2
[[[.,.],[[[[.,.],.],.],.]],.]=>2
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>2
[[[.,[.,.]],[.,[[.,.],.]]],.]=>2
[[[.,[.,.]],[[.,.],[.,.]]],.]=>3
[[[.,[.,.]],[[.,[.,.]],.]],.]=>2
[[[.,[.,.]],[[[.,.],.],.]],.]=>2
[[[[.,.],.],[.,[.,[.,.]]]],.]=>2
[[[[.,.],.],[.,[[.,.],.]]],.]=>2
[[[[.,.],.],[[.,.],[.,.]]],.]=>3
[[[[.,.],.],[[.,[.,.]],.]],.]=>2
[[[[.,.],.],[[[.,.],.],.]],.]=>2
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>2
[[[.,[.,[.,.]]],[[.,.],.]],.]=>2
[[[.,[[.,.],.]],[.,[.,.]]],.]=>2
[[[.,[[.,.],.]],[[.,.],.]],.]=>2
[[[[.,.],[.,.]],[.,[.,.]]],.]=>3
[[[[.,.],[.,.]],[[.,.],.]],.]=>3
[[[[.,[.,.]],.],[.,[.,.]]],.]=>2
[[[[.,[.,.]],.],[[.,.],.]],.]=>2
[[[[[.,.],.],.],[.,[.,.]]],.]=>2
[[[[[.,.],.],.],[[.,.],.]],.]=>2
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>2
[[[.,[.,[[.,.],.]]],[.,.]],.]=>2
[[[.,[[.,.],[.,.]]],[.,.]],.]=>3
[[[.,[[.,[.,.]],.]],[.,.]],.]=>2
[[[.,[[[.,.],.],.]],[.,.]],.]=>2
[[[[.,.],[.,[.,.]]],[.,.]],.]=>3
[[[[.,.],[[.,.],.]],[.,.]],.]=>3
[[[[.,[.,.]],[.,.]],[.,.]],.]=>3
[[[[[.,.],.],[.,.]],[.,.]],.]=>3
[[[[.,[.,[.,.]]],.],[.,.]],.]=>2
[[[[.,[[.,.],.]],.],[.,.]],.]=>2
[[[[[.,.],[.,.]],.],[.,.]],.]=>3
[[[[[.,[.,.]],.],.],[.,.]],.]=>2
[[[[[[.,.],.],.],.],[.,.]],.]=>2
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>1
[[[.,[.,[.,[[.,.],.]]]],.],.]=>1
[[[.,[.,[[.,.],[.,.]]]],.],.]=>2
[[[.,[.,[[.,[.,.]],.]]],.],.]=>1
[[[.,[.,[[[.,.],.],.]]],.],.]=>1
[[[.,[[.,.],[.,[.,.]]]],.],.]=>2
[[[.,[[.,.],[[.,.],.]]],.],.]=>2
[[[.,[[.,[.,.]],[.,.]]],.],.]=>2
[[[.,[[[.,.],.],[.,.]]],.],.]=>2
[[[.,[[.,[.,[.,.]]],.]],.],.]=>1
[[[.,[[.,[[.,.],.]],.]],.],.]=>1
[[[.,[[[.,.],[.,.]],.]],.],.]=>2
[[[.,[[[.,[.,.]],.],.]],.],.]=>1
[[[.,[[[[.,.],.],.],.]],.],.]=>1
[[[[.,.],[.,[.,[.,.]]]],.],.]=>2
[[[[.,.],[.,[[.,.],.]]],.],.]=>2
[[[[.,.],[[.,.],[.,.]]],.],.]=>3
[[[[.,.],[[.,[.,.]],.]],.],.]=>2
[[[[.,.],[[[.,.],.],.]],.],.]=>2
[[[[.,[.,.]],[.,[.,.]]],.],.]=>2
[[[[.,[.,.]],[[.,.],.]],.],.]=>2
[[[[[.,.],.],[.,[.,.]]],.],.]=>2
[[[[[.,.],.],[[.,.],.]],.],.]=>2
[[[[.,[.,[.,.]]],[.,.]],.],.]=>2
[[[[.,[[.,.],.]],[.,.]],.],.]=>2
[[[[[.,.],[.,.]],[.,.]],.],.]=>3
[[[[[.,[.,.]],.],[.,.]],.],.]=>2
[[[[[[.,.],.],.],[.,.]],.],.]=>2
[[[[.,[.,[.,[.,.]]]],.],.],.]=>1
[[[[.,[.,[[.,.],.]]],.],.],.]=>1
[[[[.,[[.,.],[.,.]]],.],.],.]=>2
[[[[.,[[.,[.,.]],.]],.],.],.]=>1
[[[[.,[[[.,.],.],.]],.],.],.]=>1
[[[[[.,.],[.,[.,.]]],.],.],.]=>2
[[[[[.,.],[[.,.],.]],.],.],.]=>2
[[[[[.,[.,.]],[.,.]],.],.],.]=>2
[[[[[[.,.],.],[.,.]],.],.],.]=>2
[[[[[.,[.,[.,.]]],.],.],.],.]=>1
[[[[[.,[[.,.],.]],.],.],.],.]=>1
[[[[[[.,.],[.,.]],.],.],.],.]=>2
[[[[[[.,[.,.]],.],.],.],.],.]=>1
[[[[[[[.,.],.],.],.],.],.],.]=>1
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>3
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>3
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>4
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>3
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>3
[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>3
[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>3
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>4
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>3
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>3
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>2
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>1
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>2
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>2
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>2
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>3
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>1
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>2
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>1
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>1
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>2
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>1
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>1
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>2
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>2
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>3
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>2
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>2
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>3
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>2
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>4
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>4
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>3
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>3
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>3
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>4
[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>3
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>3
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>3
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>3
[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>4
[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>4
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>3
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>3
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>2
[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>3
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>4
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>2
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>3
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>3
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>2
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>3
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>4
[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>3
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>3
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>3
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>4
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>3
[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>3
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>3
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>2
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>3
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>3
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>2
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>2
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>3
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>2
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>3
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>3
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>3
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>3
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>3
[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>3
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>2
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>3
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>2
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>4
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>4
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>3
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>3
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>2
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>2
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>2
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>4
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>3
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>3
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>2
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>2
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>3
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>3
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>3
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>3
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>3
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>3
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>4
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>3
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>3
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>4
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>3
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>2
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>3
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>2
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>3
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>2
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>3
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>3
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>3
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>4
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>4
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>3
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>3
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>3
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>3
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>3
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>3
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>3
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>2
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>2
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>2
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>2
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>3
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>4
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>3
[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>4
[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>3
[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>3
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>4
[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>4
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>3
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>3
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>4
[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>4
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>4
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>3
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>3
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>3
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>2
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>3
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>2
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>2
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>3
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>2
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>2
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>1
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>1
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>2
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>1
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>1
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>2
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>1
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>3
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>2
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>3
[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>2
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>3
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>2
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>2
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>1
[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>3
[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>3
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>2
[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>3
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>4
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>3
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>3
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>3
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>2
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>3
[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>3
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>3
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>2
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>3
[[[[[[[[.,.],.],.],.],.],.],.],.]=>1
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>1
[[[[.,.],.],[.,.]],[[.,.],[.,[.,.]]]]=>4
[.,[[[[.,.],.],[.,.]],[[.,.],[.,.]]]]=>4
[[[.,[.,.]],[.,.]],[[.,.],[.,[.,.]]]]=>4
[.,[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]]=>4
[[[.,.],[[.,.],.]],[[.,.],[.,[.,.]]]]=>4
[[[.,.],[.,.]],[[[.,.],[.,[.,.]]],.]]=>4
[.,[[[.,.],[[.,.],.]],[[.,.],[.,.]]]]=>4
[.,[[[.,.],[.,.]],[[[.,.],[.,.]],.]]]=>4
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>1
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>2
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>2
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>1
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>3
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]=>2
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]=>2
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>1
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>2
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>1
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>2
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]=>1
[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]=>2
[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>2
[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>3
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>1
[[[[.,.],[.,.]],[.,.]],[[.,.],[.,[.,.]]]]=>5
[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]]=>5
[[[[[.,.],.],.],[.,.]],[[.,.],[.,[.,.]]]]=>4
[.,[[[[[.,.],.],.],[.,.]],[[.,.],[.,.]]]]=>4
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>1
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>5
[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]=>4
[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]=>4
[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]=>4
[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]=>3
[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]=>4
[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]=>3
[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]=>4
[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]=>3
[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]=>4
[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]=>3
[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]=>3
[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]=>3
[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]=>2
[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]=>4
[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]=>3
[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]=>3
[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]=>3
[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]=>2
[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]=>4
[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]=>3
[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]=>3
[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]=>2
[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]=>4
[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]=>3
[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]=>3
[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]=>3
[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]=>2
[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]=>4
[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]=>3
[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]=>3
[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]=>3
[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]=>2
[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.]=>3
[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.]=>2
[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]=>3
[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]=>2
[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]=>3
[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]=>2
[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]=>2
[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]=>2
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]=>1
[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]]=>2
[.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]]=>3
[.,[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]]=>4
[.,[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]]=>3
[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]]=>4
[.,[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]]]=>4
[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]]=>5
[.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]]=>4
[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]]=>3
[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]=>4
[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]]=>5
[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]]=>4
[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]]=>5
[[.,[.,.]],[[.,[[.,[[.,.],[.,.]]],.]],.]]=>3
[[.,[.,.]],[[.,[[[.,.],[.,.]],[.,.]]],.]]=>4
[[.,[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]]=>5
[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]]=>4
[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]=>5
[[.,[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]],.]=>3
[[.,[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]],.]=>4
[[[.,[.,.]],[[.,[[.,.],[.,.]]],.]],[.,.]]=>4
[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]=>5
[[.,[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]],.]=>3
[[.,[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]],.]=>4
[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]=>5
[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[.,.]]=>4
[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]=>5
[[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]],.]=>2
[[.,[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]],.]=>3
[[.,[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.]=>4
[[.,[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]],.]=>3
[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.]=>4
[[[.,.],[.,.]],[.,[[.,[[.,.],[.,.]]],.]]]=>4
[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]=>5
[[[.,[[.,.],[.,.]]],.],[.,[[.,.],[.,.]]]]=>4
[[[[.,.],[.,.]],[.,.]],[.,[[.,.],[.,.]]]]=>5
[[[.,[[.,[[.,[.,.]],[.,.]]],.]],.],[.,.]]=>3
[[[.,[[[.,[.,.]],[.,.]],[.,.]]],.],[.,.]]=>4
[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[.,.]]=>5
[[[[.,[[.,[.,.]],[.,.]]],.],[.,.]],[.,.]]=>4
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>5
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>2
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>2
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>1
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>2
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>1
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>2
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>1
[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]=>2
[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]=>2
[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]=>2
[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]=>3
[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]]=>2
[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]]=>3
[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]]=>2
[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]]=>3
[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]]=>2
[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>3
[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>3
[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>3
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]=>4
[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>2
[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]=>3
[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]=>3
[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>3
[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>4
[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]=>2
[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>3
[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]]=>3
[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]]=>4
[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>2
[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>3
[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>3
[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>3
[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>4
[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>2
[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]]=>3
[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]]=>3
[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>3
[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]=>4
[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]]=>3
[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>4
[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>3
[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>4
[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]]=>3
[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]=>4
[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>4
[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]=>4
[[[[.,.],[.,.]],[[.,.],.]],[[.,.],[.,[.,.]]]]=>5
[.,[[[[.,.],[.,.]],[[.,.],.]],[[.,.],[.,.]]]]=>5
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>2
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>1
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>1
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>2
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]=>6
[[.,.],[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]]=>5
[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]]=>5
[[.,.],[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]]=>5
[[.,.],[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]]=>4
[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]]=>5
[[.,.],[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]]=>4
[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]]=>5
[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]]=>4
[[.,.],[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]]=>5
[[.,.],[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]]=>4
[[.,.],[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]]=>4
[[.,.],[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]]=>4
[[.,.],[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]]=>3
[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]]=>5
[[.,.],[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]]=>4
[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]]=>4
[[.,.],[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]]=>4
[[.,.],[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]]=>3
[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]]=>5
[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]]=>4
[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]]=>4
[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]]=>3
[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]]=>5
[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]]=>4
[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]]=>4
[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]]=>4
[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]]=>3
[[.,.],[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]]=>5
[[.,.],[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]]=>4
[[.,.],[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]]=>4
[[.,.],[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]]=>4
[[.,.],[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]]=>3
[[.,.],[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.]]=>4
[[.,.],[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.]]=>3
[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]]=>4
[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]]=>3
[[.,.],[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]]=>4
[[.,.],[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]]=>3
[[.,.],[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]]=>3
[[.,.],[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]]=>3
[[.,.],[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]]=>2
[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>5
[[.,[[.,.],.]],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]=>4
[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]=>4
[[.,[[.,.],.]],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]=>4
[[.,[[.,.],.]],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]=>3
[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]=>4
[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]=>3
[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]=>4
[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]=>3
[[.,[[.,.],.]],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]=>4
[[.,[[.,.],.]],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]=>3
[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]=>3
[[.,[[.,.],.]],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]=>3
[[.,[[.,.],.]],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]=>2
[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],[[.,.],.]]]]=>5
[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,[[.,.],.]],.]]]=>4
[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],[[.,.],.]]]=>4
[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],[[.,.],.]]],.]]=>4
[[.,[[.,.],[[.,.],.]]],[[.,[[.,[[.,.],.]],.]],.]]=>3
[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],[[.,.],.]]]]=>4
[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,[[.,.],.]],.]]]=>3
[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],[[.,.],.]]]=>3
[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],[[.,.],.]]],.]]=>3
[[.,[[.,[[.,.],.]],.]],[[.,[[.,[[.,.],.]],.]],.]]=>2
[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],[[.,.],.]]]=>5
[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,[[.,.],.]],.]]=>4
[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],[[.,.],.]]]=>4
[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],.]]=>3
[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],[[.,.],.]]]=>4
[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,[[.,.],.]],.]]=>3
[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],[[.,.],.]]]=>4
[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,[[.,.],.]],.]]=>3
[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],[[.,.],.]]]=>3
[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,[[.,.],.]],.]]=>2
[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],[[.,.],.]]=>5
[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],[[.,.],.]]=>4
[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],[[.,.],.]]=>4
[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],[[.,.],.]]=>4
[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],[[.,.],.]]=>3
[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],[[.,.],.]]=>4
[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],[[.,.],.]]=>3
[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],[[.,.],.]]=>4
[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],[[.,.],.]]=>3
[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],[[.,.],.]]=>4
[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],[[.,.],.]]=>3
[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],[[.,.],.]]=>3
[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],[[.,.],.]]=>3
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[[.,.],.]]=>2
[[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]],.]=>5
[[.,[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]],.]=>4
[[.,[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]],.]=>4
[[.,[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]],.]=>4
[[.,[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]],.]=>3
[[.,[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]],.]=>4
[[.,[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]],.]=>3
[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]],.]=>4
[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]],.]=>3
[[.,[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]],.]=>4
[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]],.]=>3
[[.,[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]],.]=>3
[[.,[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]],.]=>3
[[.,[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]],.]=>2
[[.,[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]],.]=>4
[[.,[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]],.]=>3
[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]],.]=>3
[[.,[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]],.]=>3
[[.,[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]],.]=>2
[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]],.]=>4
[[.,[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]],.]=>3
[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]],.]=>3
[[.,[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]],.]=>2
[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]],.]=>4
[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]],.]=>3
[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]],.]=>3
[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]],.]=>3
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]],.]=>2
[[.,[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]],.]=>4
[[.,[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]],.]=>3
[[.,[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]],.]=>3
[[.,[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]],.]=>3
[[.,[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]],.]=>2
[[.,[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.]],.]=>3
[[.,[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.]],.]=>2
[[.,[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]],.]=>3
[[.,[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]],.]=>2
[[.,[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]],.]=>3
[[.,[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]],.]=>2
[[.,[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]],.]=>2
[[.,[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]],.]=>2
[[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]],.]=>1
[.,[[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]],.]]=>2
[.,[[.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]],.]]=>3
[.,[[.,[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]],.]]=>4
[.,[[.,[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]],.]]=>3
[.,[[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]],.]]=>4
[.,[[.,[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]]],.]]=>4
[.,[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.]]=>5
[.,[[.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]],.]]=>4
[.,[[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]],.]]=>5
[.,[[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]],.]]=>3
[.,[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.]]=>4
[.,[[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]],.]]=>5
[.,[[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]],.]]=>4
[.,[[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]],.]]=>5
[.,[[[.,.],[.,.]],[[.,[[.,[[.,.],[.,.]]],.]],.]]]=>4
[.,[[[.,.],[.,.]],[[.,[[[.,.],[.,.]],[.,.]]],.]]]=>5
[.,[[[.,[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]],.]]=>5
[.,[[[.,.],[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]]]=>5
[.,[[[.,.],[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]]=>6
[.,[[[.,[[.,.],[.,.]]],.],[[.,[[.,.],[.,.]]],.]]]=>4
[.,[[[.,[[.,.],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]]=>5
[.,[[[[.,.],[.,.]],[.,.]],[[.,[[.,.],[.,.]]],.]]]=>5
[.,[[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]]]=>6
[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[[.,.],[.,.]]]]=>4
[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[[.,.],[.,.]]]]=>5
[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]]=>6
[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[[.,.],[.,.]]]]=>5
[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]]=>6
[.,[[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.],[.,.]]]=>3
[.,[[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.],[.,.]]]=>4
[.,[[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.],[.,.]]]=>5
[.,[[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.],[.,.]]]=>4
[.,[[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.],[.,.]]]=>5
[.,[[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]],[.,.]]]=>5
[.,[[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]]=>6
[.,[[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]],[.,.]]]=>5
[.,[[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]]]=>6
[.,[[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]],[.,.]]]=>4
[.,[[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]],[.,.]]]=>5
[.,[[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]]=>6
[.,[[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]],[.,.]]]=>5
[.,[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]]=>6
[[.,[.,.]],[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]]=>3
[[.,[.,.]],[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]]=>4
[[.,[.,.]],[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]]=>5
[[.,[.,.]],[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]]=>4
[[.,[.,.]],[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]]=>5
[[.,[.,.]],[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]]]=>5
[[.,[.,.]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]]=>6
[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]]=>5
[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]]=>6
[[.,[.,.]],[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]]=>4
[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]=>5
[[.,[.,.]],[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]]=>6
[[.,[.,.]],[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]]=>5
[[.,[.,.]],[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]]=>6
[[.,[[.,[.,.]],[[.,[[.,[[.,.],[.,.]]],.]],.]]],.]=>3
[[.,[[.,[.,.]],[[.,[[[.,.],[.,.]],[.,.]]],.]]],.]=>4
[[.,[[.,.],[.,.]]],[[[.,.],[.,.]],[[.,.],[.,.]]]]=>6
[[.,[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]]],.]=>4
[[.,[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]],.]=>5
[[[.,[.,.]],[[.,[[.,[[.,.],[.,.]]],.]],.]],[.,.]]=>4
[[[.,[.,.]],[[.,[[[.,.],[.,.]],[.,.]]],.]],[.,.]]=>5
[[[.,[.,.]],[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]]=>6
[[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]],[.,.]]=>5
[[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]]=>6
[[.,[[.,[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]],.]],.]=>3
[[.,[[.,[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]],.]],.]=>4
[[.,[[[.,[.,.]],[[.,[[.,.],[.,.]]],.]],[.,.]]],.]=>4
[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]],.]=>5
[[[.,[.,.]],[[.,.],[.,.]]],[[.,[[.,.],[.,.]]],.]]=>5
[[[.,[.,.]],[[.,.],[.,.]]],[[[.,.],[.,.]],[.,.]]]=>6
[[[.,[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]],.],[.,.]]=>4
[[[.,[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]],.],[.,.]]=>5
[[[[.,[.,.]],[[.,[[.,.],[.,.]]],.]],[.,.]],[.,.]]=>5
[[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]],[.,.]]=>6
[[.,[[.,[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]],.]],.]=>3
[[.,[[.,[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]],.]],.]=>4
[[.,[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]],.]=>5
[[.,[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[.,.]]],.]=>4
[[.,[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]],.]=>5
[[[.,[.,.]],[[.,[[.,.],[.,.]]],.]],[[.,.],[.,.]]]=>5
[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]]=>6
[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[.,.],[.,.]]]=>5
[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]]=>6
[[[.,[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]],.],[.,.]]=>4
[[[.,[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]],.],[.,.]]=>5
[[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]]=>6
[[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[.,.]],[.,.]]=>5
[[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]]=>6
[[.,[[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]],.]],.]=>2
[[.,[[.,[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]],.]],.]=>3
[[.,[[.,[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.]],.]=>4
[[.,[[.,[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]],.]],.]=>3
[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.]],.]=>4
[[.,[[[.,.],[.,.]],[.,[[.,[[.,.],[.,.]]],.]]]],.]=>4
[[.,[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.]=>5
[[.,[[[.,[[.,.],[.,.]]],.],[.,[[.,.],[.,.]]]]],.]=>4
[[.,[[[[.,.],[.,.]],[.,.]],[.,[[.,.],[.,.]]]]],.]=>5
[[.,[[[.,[[.,[[.,[.,.]],[.,.]]],.]],.],[.,.]]],.]=>3
[[.,[[[.,[[[.,[.,.]],[.,.]],[.,.]]],.],[.,.]]],.]=>4
[[.,[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[.,.]]],.]=>5
[[.,[[[[.,[[.,[.,.]],[.,.]]],.],[.,.]],[.,.]]],.]=>4
[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]],.]=>5
[[[.,.],[.,.]],[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]]=>4
[[[.,.],[.,.]],[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]]=>5
[[[.,[.,.]],[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.]=>5
[[[.,.],[.,.]],[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]]=>5
[[[.,.],[.,.]],[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]]=>6
[[[.,[[.,.],[.,.]]],.],[.,[[.,[[.,.],[.,.]]],.]]]=>4
[[[.,[[.,.],[.,.]]],.],[.,[[[.,.],[.,.]],[.,.]]]]=>5
[[[[.,.],[.,.]],[.,.]],[.,[[.,[[.,.],[.,.]]],.]]]=>5
[[[[.,.],[.,.]],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]=>6
[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,[[.,.],[.,.]]]]=>4
[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,[[.,.],[.,.]]]]=>5
[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[[.,.],[.,.]]]=>6
[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,[[.,.],[.,.]]]]=>5
[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,[[.,.],[.,.]]]]=>6
[[[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]],.],[.,.]]=>3
[[[.,[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]],.],[.,.]]=>4
[[[.,[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.],[.,.]]=>5
[[[.,[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]],.],[.,.]]=>4
[[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.],[.,.]]=>5
[[[[.,.],[.,.]],[.,[[.,[[.,.],[.,.]]],.]]],[.,.]]=>5
[[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]],[.,.]]=>6
[[[[.,[[.,.],[.,.]]],.],[.,[[.,.],[.,.]]]],[.,.]]=>5
[[[[[.,.],[.,.]],[.,.]],[.,[[.,.],[.,.]]]],[.,.]]=>6
[[[[.,[[.,[[.,[.,.]],[.,.]]],.]],.],[.,.]],[.,.]]=>4
[[[[.,[[[.,[.,.]],[.,.]],[.,.]]],.],[.,.]],[.,.]]=>5
[[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[.,.]],[.,.]]=>6
[[[[[.,[[.,[.,.]],[.,.]]],.],[.,.]],[.,.]],[.,.]]=>5
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>6
[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]]=>1
[.,[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],.]]=>2
[.,[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],.]]=>2
[.,[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],.]]=>2
[.,[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],.]]=>3
[.,[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],.]]=>2
[.,[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],.]]=>3
[.,[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.]]=>2
[.,[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],.]]=>3
[.,[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],.]]=>2
[.,[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],.]]=>3
[.,[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],.]]=>3
[.,[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],.]]=>3
[.,[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],.]]=>4
[.,[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>2
[.,[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]=>3
[.,[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]=>3
[.,[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]=>3
[.,[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]=>4
[.,[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],.]]=>2
[.,[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],.]]=>3
[.,[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],.]]=>3
[.,[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],.]]=>4
[.,[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],.]]=>2
[.,[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],.]]=>3
[.,[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],.]]=>3
[.,[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],.]]=>3
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],.]]=>4
[.,[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],.]]=>2
[.,[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],.]]=>3
[.,[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],.]]=>3
[.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]]=>3
[.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]]=>4
[.,[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],.]]=>3
[.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>4
[.,[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]]=>3
[.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>4
[.,[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],.]]=>3
[.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]]=>4
[.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>4
[.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]]=>4
[.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]]=>5
[[.,[.,.]],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>2
[[.,[.,.]],[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]=>3
[[.,[.,.]],[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]=>3
[[.,[.,.]],[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]=>3
[[.,[.,.]],[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]=>4
[[.,[.,.]],[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]]=>3
[[.,[.,.]],[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]]=>4
[[.,[.,.]],[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]]=>3
[[.,[.,.]],[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]]=>4
[[.,[.,.]],[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]]=>3
[[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>4
[[.,[.,.]],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>4
[[.,[.,.]],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>4
[[.,[.,.]],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]=>5
[[.,[[.,[.,.]],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>2
[[.,[[.,[.,.]],.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]=>3
[[.,[[.,[.,.]],.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]=>3
[[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>3
[[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>4
[[[.,[.,.]],[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>3
[[[.,[.,.]],[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]=>4
[[[.,[.,.]],[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]=>4
[[[.,[.,.]],[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>4
[[[.,[.,.]],[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>5
[[.,[[.,[[.,[.,.]],.]],.]],[[.,[[.,[.,.]],.]],.]]=>2
[[.,[[.,[[.,[.,.]],.]],.]],[[[.,[.,.]],[.,.]],.]]=>3
[[.,[[[.,[.,.]],[.,.]],.]],[[.,[[.,[.,.]],.]],.]]=>3
[[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>4
[[[.,[.,.]],[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]=>3
[[[.,[.,.]],[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>4
[[[.,[[.,[.,.]],.]],[.,.]],[[.,[[.,[.,.]],.]],.]]=>3
[[[.,[[.,[.,.]],.]],[.,.]],[[[.,[.,.]],[.,.]],.]]=>4
[[[[.,[.,.]],[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]]=>4
[[[[.,[.,.]],[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]]=>5
[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[[.,[.,.]],.]]=>2
[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[[.,[.,.]],.]]=>3
[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>3
[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]]=>3
[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>4
[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>3
[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>4
[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>3
[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>4
[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[[.,[.,.]],.]]=>3
[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>4
[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>4
[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>4
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>5
[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],[.,.]]=>2
[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],[.,.]]=>3
[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],[.,.]]=>3
[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],[.,.]]=>3
[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],[.,.]]=>4
[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>3
[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],[.,.]]=>4
[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],[.,.]]=>3
[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],[.,.]]=>4
[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],[.,.]]=>3
[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],[.,.]]=>4
[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>4
[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],[.,.]]=>4
[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]]=>5
[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>3
[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]]=>4
[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]]=>4
[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>4
[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]=>5
[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],[.,.]]=>3
[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>4
[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]]=>4
[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>5
[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],[.,.]]=>3
[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>4
[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>4
[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>4
[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>5
[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],[.,.]]=>3
[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],[.,.]]=>4
[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],[.,.]]=>4
[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],[.,.]]=>4
[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],[.,.]]=>5
[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]]=>4
[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]=>5
[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>4
[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>5
[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],[.,.]]=>4
[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],[.,.]]=>5
[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]=>5
[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],[.,.]]=>5
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Description
The number of leaf nodes in a binary tree.
Equivalently, the number of cherries [1] in the complete binary tree.
The number of binary trees of size $n$, at least $1$, with exactly one leaf node for is $2^{n-1}$, see [2].
The number of binary tree of size $n$, at least $3$, with exactly two leaf nodes is $n(n+1)2^{n-2}$, see [3].
Equivalently, the number of cherries [1] in the complete binary tree.
The number of binary trees of size $n$, at least $1$, with exactly one leaf node for is $2^{n-1}$, see [2].
The number of binary tree of size $n$, at least $3$, with exactly two leaf nodes is $n(n+1)2^{n-2}$, see [3].
References
[1] Billey, S., Konvalinka, M., Matsen, F. A. I. On the enumeration of tanglegrams and tangled chains arXiv:1507.04976
[2] Powers of 2: a(n) = 2^n. OEIS:A000079
[3] a(n) = n*(n+1)*2^(n-2). OEIS:A001788
[2] Powers of 2: a(n) = 2^n. OEIS:A000079
[3] a(n) = n*(n+1)*2^(n-2). OEIS:A001788
Code
def statistic(B):
if B == BinaryTree():
return 0
if B == BinaryTree([]):
return 1
return sum(statistic(S) for S in B)
# alternative implementation
# BinaryTree -> Bool
def is_leaf(b):
return b == BinaryTree('.')
# BinaryTree -> Int
def leaf_count(b):
if is_leaf(b):
return 0
if is_leaf(b[0]) and is_leaf(b[1]):
return 1
return 0
# (Num a) => a -> a -> a
def add(a, b):
return a + b
# (a -> a -> a) -> (BinaryTree -> a) -> BinaryTree -> a
def fold_tree(f, g, b):
if is_leaf(b):
return g(b)
else:
return f(g(b), f(fold_tree(f, g, b[0]), fold_tree(f, g, b[1])))
for n in [0..7]:
for b in BinaryTrees(n):
indiv_count = fold_tree(add, leaf_count, b)
print b, '=>', indiv_count
Created
May 16, 2014 at 09:02 by Joseph Ching
Updated
Mar 31, 2019 at 22:07 by Martin Rubey
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!