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;
    string s;
    cin >>n >>s;
    int nw=0,nb=0,nw0=0,nb0=0,ans;
    for(auto&& w:s){
        if(w=='.')nw++;
    }
    nb=s.size()-nw;
    nb0=nw;
    nw0=0; 
    ans=nb0;
    for(int i=0;i<n;i++){
        if(s[i]=='.'){
            nb0--;
        }else{
            nw0++;
        }
        ans=min(ans,nb0+nw0);
    }


    cout<<ans<<endl;
}