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,ans(0),sum(0);
  	scanf("%d",&N);
  	char isi[N];
  	scanf("%s",isi);
  	for(int i = 0 ; i < N ; i ++){
    	if(isi[i] == '.') ans ++;
    }
  	sum = ans;
  	for(int i = 0 ; i < N ; i ++){
      	if(isi[i] == '#') sum ++;
      	if(isi[i] == '.') sum --;
      	if(sum < ans) ans = sum;
    }
  	printf("%d",ans);
}