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) throws Exception {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		String s = sc.next();
		char[] str = s.toCharArray();
		sc.close();

		int[] cnt = new int[n + 2];
		boolean flg = false;
		int idx = 0;
		for (int i = 0; i < n; i++) {
			if (flg) {
				if (str[i] == '.') {
					idx++;
					flg = !flg;
				}
			} else {
				if (str[i] == '#') {
					idx++;
					flg = !flg;
				}
			}
			cnt[idx]++;
		}
		if (idx % 2 == 0) {
			idx++;
		}

		int[] sum = new int[idx + 1];
		sum[0] = cnt[0];
		sum[1] = cnt[1];
		for (int i = 2; i <= idx; i++) {
			sum[i] = sum[i - 2] + cnt[i];
		}

		int ans = Integer.MAX_VALUE;
		for (int i = 0; i <= idx; i++) {
			if (i % 2 == 0) {
				int w = sum[idx - 1] - sum[i];
				int b = 0;
				if (i > 0) {
					b = sum[i - 1];
				}
				ans = Math.min(ans, w + b);
			} else {
				int w = sum[idx - 1] - sum[i - 1];
				int b = sum[i];
				ans = Math.min(ans, w + b);
			}
		}
		System.out.println(ans);
	}
}