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) {
        // C - Stones

        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();
        String s = sc.next();

        char[] c = s.toCharArray();

        int min = n;
        int[] countB = new int[n + 1];
        int[] countW = new int[n + 1];

        for (int i = 0; i <= n; i++) {
            if (i > 0) {
                countB[i] = countB[i - 1];
                if (c[i - 1] == '#') ++countB[i];
            } else {
                countB[i] = 0;
            }
        }

        for (int j = n; j >= 0; j--) {
            if (j < n) {
                countW[j] = countW[j + 1];
                if (c[j] == '.') ++countW[j];
            } else {
                countW[j] = 0;
            }
            if (min > (countB[j] + countW[j])) min = countB[j] + countW[j];
        }

        System.out.println(min);
    }
}