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<stdio.h>

int main(){
int n,i,ans=0,juge=0;
  
 scanf("%d",&n);
  
 char s[n];
  
 scanf("%s",s);
  
 for(i=0;i<n;i++){
    	if(s[i]=='.') {
          ans++;
        }
    }
 juge=ans;
 for(i=0;i<n;i++){
    	if(s[i]=='#') {juge++;}
      	else {juge--;}
      	if(juge<ans) {ans=juge;}
    }
  printf("%d",ans);
	return 0;
}