Nikita and string

## 题目描述 Nikita发现了一个只含 'a' 与 'b' 的字符串。Nikita认为，如果一个字符串可以分为三段，第1、3段只含'a'，第2段只含'b'（每段都能为空），则这个字符串是美丽的。Nikita想删除（不是改变）某些字符，把输入的字符串变成美丽的。（可以不改变原串） ## 输入描述 一行，原字符串。 ## 输出描述 一行，可能的最大美丽字符串长度。

One day Nikita found the string containing letters "a" and "b" only. Nikita thinks that string is beautiful if it can be cut into $ 3 $ strings (possibly empty) without changing the order of the letters, where the $ 1 $ -st and the $ 3 $ -rd one contain only letters "a" and the $ 2 $ -nd contains only letters "b". Nikita wants to make the string beautiful by removing some (possibly none) of its characters, but without changing their order. What is the maximum length of the string he can get?

The first line contains a non-empty string of length not greater than $ 5000 $ containing only lowercase English letters "a" and "b".

Print a single integer — the maximum possible size of beautiful string Nikita can get.

abba

4

bab

2

It the first sample the string is already beautiful. In the second sample he needs to delete one of "b" to make it beautiful.