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 n,a[200005];
int f[200005][2];
int main(){

	cin>>n;
	for(int i=1;i<=n;i++){
		char x;
		cin>>x;
		if(x=='#')
			a[i]=1;
		else
			a[i]=0;
	}
	for(int i=1;i<=n;i++){
		if(a[i]==1){
			f[i][1]=min(f[i-1][0],f[i-1][1]);
			f[i][0]=f[i-1][0]+1;
		}
		if(a[i]==0){
			f[i][0]=f[i-1][0];
			f[i][1]=min(f[i-1][0],f[i-1][1])+1;
		}
	}
	cout<<min(f[n][0],f[n][1])<<endl;
}