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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner scan = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int N = scan.nextInt();
        String S = scan.next();
        char[] data = S.toCharArray();
        int[] sum = new int[N+1];
        Arrays.fill(sum, 0);
        int answer = Integer.MAX_VALUE;
        boolean badfound = false;
        int whitecount = 0;
        boolean blackfound = false;
        for (int i = 0; i < N; i++) {
            if (blackfound && data[i] == '.') {
                whitecount += 1;
            }
            if (i < N - 1 && data[i] == '#' && data[i+1] == '.') {
                badfound = true;
            }
            if (data[i] == '#') {
                blackfound = true;
                sum[i+1] += sum[i] + 1;
                continue;
            }
            sum[i+1] += sum[i];
        }
        if (badfound) {
            for (int i = 0; i < N; i++) {
                answer = Math.min(sub(N, sum, i + 1), answer);
            }
            answer = Math.min(whitecount, answer);
        } else {
            answer = 0;
        }
        System.out.println(answer);
    }
    public static int sub(int N, int[] sum, int from) {
        int blackcount_before_from = sum[from];
        int whitecount_before_from = from - sum[from];
        int whitecount_after_from = N - sum[N] - whitecount_before_from;
        return blackcount_before_from + whitecount_after_from;
    }
}