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();
        char[] s = sc.next().toCharArray();
        int[] b = new int[n];
        int[] w = new int[n];
        if(s[0] == '.') w[0] = 1;
        else b[0] = 1;
        for (int i = 1; i < n; i++) {
            b[i] = b[i-1];
            w[i] = w[i-1];
            if(s[i] == '.') w[i]++;
            else b[i]++;
        }
        int ans = Integer.MAX_VALUE;
        for (int i = 0; i <= n; i++) {
            if(i == 0){
                ans = Math.min(ans, w[n-1]);
            }else if(i == n){
                ans = Math.min(ans, b[n-1]);
            }else{
                ans = Math.min(ans, b[i-1] + (w[n-1] - w[i-1]));
            }
        }
        System.out.println(ans);
        sc.close();
    }

}