Problem: 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.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#pragma GCC diagnostic ignored "-Wunused-result"
#pragma GCC diagnostic ignored "-Wunused-function"
using namespace std;
namespace {
namespace shik {
template <class T>
void _R(T &x) {
  cin >> x;
}
void _R(int &x) { scanf("%d", &x); }
void _R(int64_t &x) { scanf("%" SCNd64, &x); }
void _R(double &x) { scanf("%lf", &x); }
void _R(char &x) { scanf(" %c", &x); }
void _R(char *x) { scanf("%s", x); }
void R() {}
template <class T, class... U>
void R(T &head, U &...tail) {
  _R(head);
  R(tail...);
}
template <class T>
void _W(const T &x) {
  cout << x;
}
void _W(const int &x) { printf("%d", x); }
void _W(const int64_t &x) { printf("%" PRId64, x); }
void _W(const double &x) { printf("%.16f", x); }
void _W(const char &x) { putchar(x); }
void _W(const char *x) { printf("%s", x); }
template <class T>
void _W(const vector<T> &x) {
  for (auto i = x.begin(); i != x.end(); _W(*i++))
    if (i != x.cbegin()) putchar(' ');
}
void W() {}
template <class T, class... U>
void W(const T &head, const U &...tail) {
  _W(head);
  putchar(sizeof...(tail) ? ' ' : '\n');
  W(tail...);
}
template <class T, class F = less<T>>
void sort_uniq(vector<T> &v, F f = F()) {
  sort(begin(v), end(v), f);
  v.resize(unique(begin(v), end(v)) - begin(v));
}
template <class T>
inline T bit(T x, int i) {
  return (x >> i) & 1;
}
template <class T>
inline bool chkmax(T &a, const T &b) {
  return b > a ? a = b, true : false;
}
template <class T>
inline bool chkmin(T &a, const T &b) {
  return b < a ? a = b, true : false;
}
template <class T>
using MaxHeap = priority_queue<T>;
template <class T>
using MinHeap = priority_queue<T, vector<T>, greater<T>>;
const int N = 5010;
char s[N];
int z[N];
void main() {
  scanf("%s", s + 1);
  int n = strlen(s + 1);
  for (int i = (1); i <= int(n); i++) z[i] = z[i - 1] + (s[i] == 'a');
  int ans = 0;
  for (int i = (0); i <= int(n); i++)
    for (int j = (i); j <= int(n); j++) {
      int c1 = z[i];
      int c2 = (j - i) - (z[j] - z[i]);
      int c3 = z[n] - z[j];
      int now = c1 + c2 + c3;
      chkmax(ans, now);
    }
  W(ans);
}
}  // namespace shik
}  // namespace
int main() {
  shik::main();
  return 0;
}