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 main(){
	int n,stone[200001],stones[200001],ans=0x7fffffff;
	char s[200001];
	scanf("%d%s",&n,s);
	for(int i=0;i<n;i++)stone[i]=s[i]=='#';
	for(int i=n;i>=0;i--)stones[i]=stones[i+1]+stone[i];
	for(int i=0;i<=n;i++)ans=min(ans,stones[0]-2*stones[i]+n-i);
	printf("%d\n",ans);
}