Problem: There are N stones arranged in a row. Every stone is painted white or black. A string S represents the color of the stones. The i-th stone from the left is white if the i-th character of S is `.`, and the stone is black if the character is `#`.

Takahashi wants to change the colors of some stones to black or white so that there will be no white stone immediately to the right of a black stone. Find the minimum number of stones that needs to be recolored.

Constraints

* 1 \leq N \leq 2\times 10^5
* S is a string of length N consisting of `.` and `#`.

Input

Input is given from Standard Input in the following format:


N
S


Output

Print the minimum number of stones that needs to be recolored.

Examples

Input

3
#.#


Output

1


Input

3
.#


Output

1


Input

5
.##.


Output

2


Input

9
.........


Output

0

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

int main(int argc, char const *argv[]) {
  int n;
  string s;
  int cnt = 0;
  cin >> n;
  cin >> s;

  for (size_t i = 0; i < n; i++) {
    if (s[i] == '.') cnt++;
  }
  int ans = cnt;

  for (size_t i = 0; i < n; i++) {
    if (s[i] == '.')
      cnt--;
    else if (s[i] == '#')
      cnt++;
    ans = min(ans, cnt);
  }

  cout << ans << endl;
  return 0;
}