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.Scanner;

public class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        sc.nextLine();
        String S = sc.nextLine();

        int[] sum = new int[N+1];
        sum[0]=0;
        for(int i=0;i<N;i++){
            if(S.charAt(i)=='#'){
                sum[i+1]=sum[i]+1;
            }else{
                sum[i+1]=sum[i];
            }
        }
        int ans=N;
        for(int i=0;i<=N;i++){
            int cnt = sum[i] + ( (N-i) - (sum[N]-sum[i]) );
            // System.out.println(cnt);
            if(ans>cnt)ans=cnt;
        }
        System.out.println(ans);
    }
}