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 sc = new Scanner(System.in);

		int n = sc.nextInt();
		String s = sc.next();
		
		int wcount = 0;
		int bcount = 0;
		
		System.out.println();
		
		char[] schar = s.toCharArray();
		
		for (int i = 0; i < n; i++) {
			if (schar[i] == '.') {
				wcount++;
			} else {
				
			}
			
		}
			
			int maxWcount = wcount; 
			
			int bwmin = maxWcount;
			
		for (int i = 0; i < n; i++) {
			if (schar[i] == '#') {
				bcount++;
			} else {
				wcount--;
			}
			
			int tmp = bcount + wcount;
			
			if (tmp < bwmin) {
				bwmin = tmp;
			}
			
		}
		
		int min = Math.min(maxWcount, bwmin);
 	
	System.out.println(min);
	}
}