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.*;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		String s = sc.next();
		sc.close();
		int min = 0;
		int shoki = 0;
		for (int i = 0; i < n; i++) {
			if (s.charAt(i) != '#') {
				shoki++;
			}
		}
		min = shoki;
		int prev = shoki;
		for (int i = 0; i < n; i++) {
			if (s.charAt(i) == '.') {
				prev--;
			} else {
				prev++;
			}
			if (prev < min)
				min = prev;
		}
		System.out.println(min);
	}
}