CF877B.Nikita and string

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题目描述

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?

输入格式

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

输出格式

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

输入输出样例

输入#1
```
abba
```
输出#1
```
4
```
输入#2
```
bab
```
输出#2
```
2
```

说明/提示

It the first sample the string is already beautiful.

In the second sample he needs to delete one of "b" to make it beautiful.

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