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<algorithm>
using namespace std;

#define ran 202202

int n;
char s[ran];
int sum[ran];

int main() {
	scanf("%d%s", &n, s);
	
	sum[0] = 0;
	for(int i=0;i<n;i++)
		sum[i+1] = sum[i] + (s[i]=='#');
	
	int ans = n;
	for(int i=0;i<=n;i++)
		ans = min(ans, sum[i] + (n-i)-(sum[n]-sum[i]));
	printf("%d\n", ans);
	
	return 0;
}