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.IOException;
import java.io.InputStreamReader;

public class Main {
	public static void main(String args[]) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

		int n = Integer.parseInt(br.readLine());

		String str[] = br.readLine().split("");

		int white[] = new int[n + 1];
		int black[] = new int[n + 1];

		for (int i = 0; i < n + 1; i++) {
			if (i - 1 >= 0) {
				if (str[i - 1].equals("#"))
					black[i] = 1 + black[i - 1];
				else
					black[i] = black[i - 1];
			}
		}

		for (int i = n; i >= 0; i--) {
			if (i + 1 < n) {
				if (str[i + 1].equals("."))
					white[i] = 1 + white[i + 1];
				else
					white[i] = white[i + 1];
			}
		}

		int ans = Integer.MAX_VALUE;

		for (int i = 0; i < n + 1; i++) {
			ans = Math.min(ans, black[i] + white[i]);
		}

		System.out.println(ans);
	}
}