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();
        String s = sc.next();

        int[] a = new int[n + 1];
        int count = 0 ;
        for (int i = 1 ; i < n + 1 ; i++) {
            if (s.substring(i - 1, i).equals("#")) {
                count++;
            }
            a[i] = count;
        }

        int min = 12345567;
        for (int i = 0 ; i < n + 1 ; i++) {
            int b = n - i - (a[n] - a[i]);
            int w = a[i];
            min = Math.min(min, b + w);
        }

        System.out.println(min);
    }

}