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 N;cin >> N;
  string S;cin >> S;
  int Bsum = 0;
  vector<int> B(N,0);
  if(S[0]=='#'){
    B[0]=1;
    Bsum ++;
  }
  for(int i=1;i<N;i++){
    if(S[i]=='#'){
      B[i] = B[i-1] + 1;
      Bsum ++;
    }else{
      B[i] = B[i-1];
    }
  }
  int ans = N - Bsum;
  for(int i=0;i<N;i++){
    ans = min(ans,B[i]+N-i-1-(Bsum-B[i]));
  }
  ans = min(ans,Bsum);
  cout << ans << endl;
}