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()
  {
    ios::sync_with_stdio(0);
      cin.tie(0);
      cout.tie(0);
    
    int n;
    string s;
    cin >> n >> s;
    int c=0;
    for(int i=0;i<n;i++) {
      if(s[i]=='.') c++;
    }
    int ans = c;
    for(int i=0;i<n;i++) {
      if(s[i]=='#') c++;
      else c--;
      ans = min(ans, c);
    } 
    cout << ans << "\n";

    return 0;
  }