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;
  string S;
  cin >> N >> S;
  vector<int> B(N+10),W(N+10);
  B[0]=0;
  for(int i=0;i<N;i++){
    B[i+1]=B[i]; if(S[i]=='#'){B[i+1]++;}
  }
  for(int i=0;i<=N;i++){W[i]=i-B[i];}
  int m=200000000;
  for(int i=0;i<N;i++){
    int a=B[i]+(W[N]-W[i+1]);
    m=min(a,m);
  }
  cout << m << endl;
}