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;

int sum[200005];
char s[200005];

int main(){
	int n;
	scanf("%d",&n);
	int i;
	scanf("%s",s + 1);
	for(i = 1;i <= n;i++)sum[i] = sum[i-1] + (s[i] == '.');
	int ans = 2147483647;
	for(i = 0;i <= n;i++)ans = min(ans,i - sum[i] + sum[n] - sum[i]);
	cout<<ans<<endl;
	return 0;
}