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 {
    private static final char BLACK = '#';
    private static final char WHITE = '.';

    public static void main(String[] args) {
        final Scanner scanner = new Scanner(System.in);
        final int length = scanner.nextInt();
        scanner.nextLine();
        final char[] chars = scanner.nextLine().toCharArray();

        int white = 0;
        int black = 0;
        for (int i = 0; i < length; i++) {
            if (chars[i] == WHITE) {
                white++;
            } else {
                black++;
            }
        }

        int result = Integer.MAX_VALUE;
        int kuroRuiseki = 0;
        for (int i = 0; i < length; i++) {
            if (chars[i] == BLACK) {
                kuroRuiseki++;
            }

            int kaeru = kuroRuiseki + length - i - 1 - (black - kuroRuiseki);

            if (kaeru >= 0 && result > kaeru) {
                result = kaeru;
            }
        }

        System.out.println(Math.min(Math.min(black, white), result));

    }
}