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,ans=INT_MAX;
  string s;
  cin >>n >>s;
  int wcount[n+1];
  wcount[0]=0;
  for(int i=0;i<n;i++){
    if(s[i]=='.')wcount[i+1]=wcount[i]+1;
    else wcount[i+1]=wcount[i];
  }
  for(int i=0;i<n+1;i++){
    ans=min(ans,i-wcount[i]+wcount[n]-wcount[i]);
  }
  cout << ans <<endl;
}