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) {
		Scanner scanner = new Scanner(System.in);
		int N = scanner.nextInt();
		String S = scanner.next();
		// N == S.length();
		int black = 0;
		int white = 0;
		for(int i = 0; i < N; i++) {
			if(S.charAt(i) == '.') {
				white++;
			}
		}
		int min = white;
		for(int i = 0; i < N; i++) {
			if(S.charAt(i) == '#') {
				black++;
			}else {
				white--;
			}
			min=Math.min(min, black+white);
		}
		System.out.println(min);
		
		scanner.close();
	}
}