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 scan=new Scanner(System.in);
		int a=scan.nextInt();
		String str=scan.next();
		int rui[]=new int[a];
		int co=0;
		int kirikaeshi=0;
		for(int i=0;i<a;i++) {
			char ch=str.charAt(i);
			if(i<a-1) {
				char ch2=str.charAt(i+1);
				if(ch!=ch2) {
					kirikaeshi++;
				}
			}
			if(ch=='#') {
				co++;
			}
			rui[i]=co;
		}
		int len=str.length();
		if(kirikaeshi==0||kirikaeshi==1&&str.charAt(0)=='.') {
			System.out.println(0);
			return;
		}
		else if(kirikaeshi==1&&str.charAt(0)=='#') {
			int min=0;
			min=Math.min(rui[a-1], len-rui[a-1]);
			System.out.println(min);
			return;
		}
		int ans=1145141919;
		for(int i=0;i<str.length();i++) {
			int change=rui[i];
			int nokori=len-i-1;
			int zerosum=rui[a-1]-rui[i];
			change+=nokori-zerosum;
			if(ans>change) {
				ans=change;
			}
		}
		System.out.println(ans);
	}
}