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(){
  long long n;
  string s;
  cin >> n >> s;
  long long w=0;
  long long bl;
  long long wr;
  
  for(long i=0; i<n; i++){
    if(s.at(i) == '.'){
      w++;
    }
  }
  
  bl=0;
  wr=w;
  long long res = bl+wr;
  
  for(long i=0; i<n; i++){
    if(s.at(i) == '.'){
      wr--;
    }else{
      bl++;
    }
    
    res = min(res,wr+bl);
  }
  cout << res << endl;
}