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<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
int main()
{
  int n,count = 0, ans = 0;
  char *s;
  scanf("%d",&n);
  s = new char[n+1];
  scanf("%s",s);

  for (int i = 0; i < n ; ++i)
    if (s[i] == '.')
      ++count;
  
  ans = count;
  for (int i = 0 ; i < n ; ++i) {
    if(s[i]=='#') ++count;
    else --count;
    ans = min(ans,count);
  }
  
  printf("%d",ans);
  delete s;
  return 0;
}