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.Collections;
import java.util.Scanner;

public class Main {
	public static String repeat(String str, int n) {
		return String.join("", Collections.nCopies(n, str));
	}

	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		sc.nextLine();
		String line = sc.nextLine();

		int diff = 0;
		String rightAnswer = repeat(".", n);
		int nextDiff = 0;

		for (int i = 0; i < n; i++) {
			if (line.charAt(i) != rightAnswer.charAt(i))
				diff++;
		}

		int best = diff;

		for (int i = n - 1; i > -1; i--) {
			if (line.charAt(i) == '#')
				nextDiff = diff - 1;
			else {
				nextDiff = diff + 1;
			}
			if (nextDiff < best) {
				best = nextDiff;
			}
			diff = nextDiff;
		}

		System.out.println(best);

		sc.close();
	}
}