1941. Essay

Mirko's latest homework assignment is writing an essay. However, he finds writing essays so boring that, after working for two hours, he realized that all he has written are `N` long words consisting entirely of letters A and B. Having accepted that he will never finish the essay in time, poor Mirko has decided to at least have some fun with it by counting nicewords.

Mirko is connecting pairs of identical letters (A with A, B with B) by drawing arches above the word. A given word is nice if each letter can be connected to exactly one other letter in such a way that no two arches intersect. Help Mirko count how many words are nice.

The first line of input contains the positive integer `N` (`1\ ≤\ N\ ≤\ 100`), the number of words written down by Mirko.

Each of the following `N` lines contains a single word consisting of letters A and B, with length between 2 and `100\ 000`, inclusive. The sum of lengths of allwords doesn't exceed `1\ 000\ 000`.

The first and only line of output must contain the number of nice words.

3 
ABAB 
AABB 
ABBA

2

3 
AAA 
AA 
AB 

1

1 
ABBABB 

1