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();
        String[] str = s.split("");

        int rightWhite = 0;
        int leftBlack = 0;
        for (int i = 0; i < str.length; i++) {
            if (".".equals(str[i])) {
                rightWhite++;
            }
        }
        int min = leftBlack + rightWhite;
        for (int i = 0; i < str.length; i++) {
            if ("#".equals(str[i])) {
                leftBlack++;
            } else {
                rightWhite--;
            }
            if ((leftBlack + rightWhite) < min) {
                min = leftBlack + rightWhite;
            }
        }
        System.out.println(min);
    }

}