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 JAVA):

Solution:
import java.util.*;
 
public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n=sc.nextInt();
        String in=sc.next();
        String []s=in.split("",0);
        String ss="";
        int count=0;
        for(int i=0;i<n;i++){
            if(!s[i].equals("#")){
                count++;
            }
        }
        int countmin=count;
        for(int i=0;i<n;i++){
            if(!s[i].equals("#"))
                count--;
            else count++;
            countmin=Math.min(count,countmin);
        }
        System.out.println(countmin);
    }
    
    
 
}class Po{
    int a,b;
    public Po(int a,int b){
        this.a=a;
        this.b=b;
    }
    public String toString(){
        return a+" "+b;
    }
}