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 num_b,num_w,w_all;
  num_b=0;
  num_w=0;
  w_all=0;
  for(int i=0;i<n;++i){
    if(s[i]=='.'){
      w_all++;
    }
  }
  int ans=w_all;
  for(int i=0;i<n;++i){
    int cal=0;
    if(s[i]=='.'){
      num_w++;
    }else{
      num_b++;
    }
    cal=num_b+w_all-num_w;
    ans=min(ans,cal);
  }

  cout << ans << endl;
  return 0;
}