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.Arrays;
import java.util.Scanner;

public class Main {

    void run() {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        String s = sc.next();
        int[] sum1 = new int[n + 1], sum2 = new int[n + 1];
        for (int i = 1; i <= n; i++) {
            sum1[i] = sum1[i - 1] + (s.charAt(n - i) == '#' ? 0 : 1);
            sum2[i] = sum2[i - 1] + (s.charAt(i - 1) == '.' ? 0 : 1);
        }

        int ans = 2 * n;
        for (int i = 0; i <= n; i++) {
            ans = Math.min(ans, sum1[i] + sum2[n - i]);
        }
        System.out.println(ans);
    }

    void debug(Object...os) {
        System.err.println(Arrays.deepToString(os));
    }

    public static void main(String[] args) {
        new Main().run();
    }
}