Physical Education

There is a physical education lesson at a school. Unfortunately, there are many classes but only one teacher, so $n$ classes take the lesson together. The students in each class form a row, and boys and girls are mixed within each row.

It is inconvenient to teach several rows separately, so the teacher decides to merge all the rows into one. The teacher can pick two rows and place all students from one of them at the end of the other, which makes one long row. The order of students inside each row cannot be changed.

Once the teacher has one single row, the students are split into two groups. Going along the row, the students say "First", "Second", "First", "Second", and so on. Students who stand in odd positions form the "First" group and go play football. Students who stand in even positions form the "Second" group and go play volleyball.

Boys like football, and girls do not. The teacher wants to arrange the students so that as many boys as possible play football. Find the maximum number of boys who can play football.

The first line contains one integer $n$ ($1 \le n \le 100,000$), the number of classes.

The next $n$ lines each describe the initial row of one class. Each line is a string of the letters B and G. B means a boy and G means a girl. The first letter of a string is the first student in that row. Each row is not empty and contains at most 100 letters.

The total number of students does not exceed $10^6$.

Print a single integer, the maximum possible number of boys who play football.

In the sample above, not all boys can play football at the same time. However, if the rows are arranged as BGG, BB, GG, GBG, then three of the four boys can play football.