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 <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <math.h>
#include <map>
using namespace std;

int main(){
int n;string s;
cin>>n>>s;
int sum[n+1];
sum[0]=0;
for(int i=1;i<=n;i++){
    sum[i]=sum[i-1]+(s[i-1]=='.');
}
int ans=n;
for(int i=0;i<=n;i++){
    int a=sum[n]+i-2*sum[i];
    ans=min(a,ans);
}
cout<<ans;

}