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 bf = null;
		bf = new BufferedReader(new InputStreamReader(System.in));
		int n,i,ans,temp = 0;
		String str;
		str = bf.readLine();
		n = Integer.parseInt(str);
		str = bf.readLine();
		for(i = 0;i < n;++i) {
			if(str.charAt(i) == '.') {
				temp++;
			}
		}
		ans = temp;
		for(i = 0;i < n;++i) {
			if(str.charAt(i) == '.') {
				temp--;
			} else {
				temp++;
			}
			if(ans > temp) {
				ans = temp;
			}
		}
		System.out.println(ans);
	}
}