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 a,e,f;
  string b;

  cin>>a>>b;
  vector<int>c(a+1),d(a+1);
  c[0]=0;
  d[0]=0;
  f=a;
  for(int i=0;i<a;i++){
      if(b[i]=='#'){
        c[i+1]=c[i]+1;
        d[i+1]=d[i];
      }
      else{
        c[i+1]=c[i];
        d[i+1]=d[i]+1;
      }
    }
 for(int i=0;i<a;i++){
f=min(f,c[i]+d[a]-d[i+1]);
 }

cout<<f<<endl;
}