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.
Examples
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：在一个只含a,b的字符串中，规定一个序列必须按序可分为三部分，第一，第三部分只包含字符a或者为空，第二部分只包含字符b或空。问满足条件的最长子序列的长度。
思路：我们可以利用前缀记录截至到每个位置处a出现的次数。然后我们可以暴力枚举（暴力的方法在代码上解释）每一种情况，维护最大值。
代码如下：
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
int a[5010],b[5010];
int main()
{
char str[5010];
scanf("%s",str);
int l=strlen(str);
for(int i=1;i<=l;i++) //计算前缀
{
a[i]=a[i-1]+(str[i-1]=='a');
b[i]=b[i-1]+(str[i-1]=='b');
}
int maxl=0;
for(int i=0;i<=l;i++)
for(int j=i;j<=l;j++)
maxl=max(maxl,a[i]+(b[j]-b[i])+(a[l]-a[j]));//维护最大值，max（以前的值，一 到前i个数中a个数+二[i,j]中b的个数 + 三 [j,l]中a的个数）
printf("%d\n",maxl);
}