407774: GYM102892 3 Infectious Letters

You have a string of length $$$n$$$. Unfortunately, some of its letters are infectious. More specifically, any "a" characters in the string have the potential to spread to any adjacent characters. At any point in time, an "a" character in the string can "infect" any of its adjacent characters, and make them an "a" character as well.

However, "b" characters are immune to the "a" characters' infection, and thus can't be changed into "a" characters.

For example, if we have the string "cabaccabdd", the second character of the string could infect the first character, turning it into another "a", but it couldn't infect the third character of the string, since it's a "b".

Your task is to determine the maximum number of $$$a$$$ characters that could exist in the string after an unlimited amount of infections.

For example, in the string "cabaccabdd" could become "aabaaaabdd" in an unlimited number of infections, which has 6 "a" characters.

The first line of input contains a single positive integer $$$n$$$ $$$(1 <= n <= 200000)$$$: the length of the string.

The next line of input contains the string.

Output the maximum number of $$$a$$$ characters that could exist in the string after an unlimited amount of infections.

Full problem: 10 points

15
bbbacxdbxyabxab

9

5
bbbbb

0

5
aabcc

2