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 <cmath>
#include <algorithm>
#include <vector>
using namespace std;
int main(){
    int n,k=1e9+7,a=0,b=0;string s;
    cin>>n>>s;
    vector<int> black(n);
    vector<int> white(n);
    for(int i=0;i<n;i++){
        if(s[i]=='#') a++;
        else b++;
        black[i]=a;white[i]=b;
    }
    for(int i=0;i<n;i++) k=min(k,black[i]+white[n-1]-white[i]);
    k=min(k,b);
    cout<<k;
}