Nikita and string

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?

Input

The first line contains a non-empty string of length not greater than 5 000 containing only lowercase English letters "a" and "b".

Output

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

Example

Input

abba

Output

4

Input

bab

Output

2

Note

It the first sample the string is already beautiful.

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

题意:在字符串中找到一个最长的可以不连续的子串， 子串是a..b..a..;

#include
    
     #include
     
      #include
      
       using namespace std;int main(){    string s;    while(cin>>s)    {        int a=0,ab=0,aba=0;        for(int i=0;i