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;
#define ll long long
inline int read() {
	int f=1,x=0;char ch=getchar();
	while(!isdigit(ch)) {if(ch=='-') f=-1;ch=getchar();}
	while(isdigit(ch)) {x=x*10+ch-'0'; ch=getchar();}
	return x*f;
}
int main() {
	int n,a=0,b=0;
	char str[200005];
	n=read();
	scanf("%s",str);
	for(int i=0;i<n;i++) {
		if(str[i]=='#')a++;
		if(str[i]=='.'&&a>0)b++,a--;
	}
	printf("%d",b);
	return 0;
}