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 <algorithm>
#include <iostream>
#include <string>
#include <vector>

using namespace std;

int main() {
  int n;
  string s;
  cin >> n >> s;
  vector<int> v(n + 1);
  for (int i = 0; i < n; i++) {
    v[i + 1] = v[i];
    if (s[i] == '#') {
      v[i + 1]++;
    }
  }
  int ans = n;
  for (int i = 0; i <= n; i++) {
    ans = min(ans, v[i] + (n - i - v[n] + v[i]));
  }
  cout << ans << endl;

  return 0;
}