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>
using namespace std;
const long long maxn = 2e6 + 6;
const long long MOD = 1e9 + 7;
bool comparator(long long i, long long j) { return (i < j); }
long long power(long long x, long long i) {
  long long ans = 1;
  while (i > 0) {
    if (i & 1) ans = (ans * x) % MOD;
    i >>= 1;
    x = (x * x) % MOD;
  }
  return ans;
}
long long power(long long x, long long i, long long mod) {
  long long ans = 1;
  while (i > 0) {
    if (i & 1) ans = (ans * x) % mod;
    i >>= 1;
    x = (x * x) % mod;
  }
  return ans;
}
long long modInverse(long long x, long long mod) {
  return power(x, mod - 2, mod);
}
bool isPalindrome(string s) {
  long long limit = s.length() / 2;
  for (long long i = 0; i < limit; i++) {
    if (s[i] != s[s.length() - i - 1]) return 0;
  }
  return true;
}
long long gcd(long long x, long long y) {
  long long t;
  while (y != 0) {
    t = x % y;
    x = y;
    y = t;
  }
  return x;
}
bool isVowel(char ch) {
  if (ch == 'a' || ch == 'i' || ch == 'e' || ch == 'u' || ch == 'o' ||
      ch == 'y') {
    return true;
  }
  return false;
}
bool isPrime(long long n) {
  long long root = sqrt(n);
  for (long long i = 2; i <= root; i++)
    if (n % i == 0) return 0;
  return 1;
}
long double getDis(long double asdfg, long double qwert, long double gfdsa,
                   long double trewq) {
  return sqrt((asdfg - gfdsa) * (asdfg - gfdsa) +
              (qwert - trewq) * (qwert - trewq));
}
long double getDisSquare(long double asdfg, long double qwert,
                         long double gfdsa, long double trewq) {
  return (asdfg - gfdsa) * (asdfg - gfdsa) + (qwert - trewq) * (qwert - trewq);
}
bool isSquareHelper(long long asdfg, long long qwert, long long gfdsa,
                    long long trewq, long long x3, long long y3, long long x4,
                    long long y4) {
  long double d1, d2, d3, d4, d5, d6;
  d1 = getDisSquare(asdfg, qwert, gfdsa, trewq);
  d2 = getDisSquare(gfdsa, trewq, x3, y3);
  d3 = getDisSquare(x3, y3, x4, y4);
  d4 = getDisSquare(x4, y4, asdfg, qwert);
  if (d1 == d2 && d1 == d3 && d1 == d4) {
    d5 = getDisSquare(asdfg, qwert, x3, y3);
    d6 = getDisSquare(gfdsa, trewq, x4, y4);
    if (d5 == d6) {
      return 1;
    }
  }
  return 0;
}
bool isSquare(long long asdfg, long long qwert, long long gfdsa,
              long long trewq, long long x3, long long y3, long long x4,
              long long y4) {
  if (isSquareHelper(asdfg, qwert, gfdsa, trewq, x3, y3, x4, y4) ||
      isSquareHelper(asdfg, qwert, gfdsa, trewq, x4, y4, x3, y3) ||
      isSquareHelper(asdfg, qwert, x3, y3, gfdsa, trewq, x4, y4))
    return 1;
  else
    return 0;
}
bool isEqualateralTriangle(long long asdfg, long long qwert, long long gfdsa,
                           long long trewq, long long x3, long long y3) {
  long long d1 = getDisSquare(asdfg, qwert, gfdsa, trewq);
  long long d2 = getDisSquare(gfdsa, trewq, x3, y3);
  long long d3 = getDisSquare(x3, y3, asdfg, qwert);
  if (d1 == d2 && d1 == d3) {
    return 1;
  } else
    return 0;
}
bool isRightAngleTriangleHelper(long long asdfg, long long qwert,
                                long long gfdsa, long long trewq, long long x3,
                                long long y3) {
  long long d1 = getDisSquare(asdfg, qwert, gfdsa, trewq);
  long long d2 = getDisSquare(gfdsa, trewq, x3, y3);
  long long d3 = getDisSquare(x3, y3, asdfg, qwert);
  if (d2 == (d1 + d3)) {
    return 1;
  }
  return 0;
}
bool isRightAngleTriangle(long long asdfg, long long qwert, long long gfdsa,
                          long long trewq, long long x3, long long y3) {
  if (isRightAngleTriangleHelper(asdfg, qwert, gfdsa, trewq, x3, y3) ||
      isRightAngleTriangleHelper(gfdsa, trewq, x3, y3, asdfg, qwert) ||
      isRightAngleTriangleHelper(x3, y3, asdfg, qwert, gfdsa, trewq))
    return 1;
  return 0;
}
bool areCollinear(long long asdfg, long long qwert, long long gfdsa,
                  long long trewq, long long x3, long long y3) {}
string s;
long long l[maxn], r[maxn];
void getInput() { cin >> s; }
long long getCount(long long i, long long j) {
  long long la, ra, midb;
  if (i == 0) {
    la = 0;
    ra = r[j + 1];
    midb = j + 1 - l[j];
  } else {
    la = l[i - 1];
    ra = r[j + 1];
    midb = (j - i + 1) - (l[j] - l[i - 1]);
  }
  return la + midb + ra;
}
void solve() {
  long long ans = 0, c = 0;
  for (long long i = 0; i < s.length(); i++) {
    if (s[i] == 'a') {
      c++;
    }
    l[i] = c;
  }
  c = 0;
  for (long long i = s.length() - 1; i >= 0; i--) {
    if (s[i] == 'a') {
      c++;
    }
    r[i] = c;
  }
  r[s.length()] = 0;
  for (long long i = 0; i < s.length(); i++) {
    for (long long j = i; j <= s.length() - 1; j++) {
      ans = max(getCount(i, j), ans);
    }
  }
  cout << max(ans, l[s.length() - 1]) << "\n";
}
signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long t = 1;
  while (t--) getInput(), solve();
  return 0;
}