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[] white=new int[N+1];
		int[] black=new int[N+1];

		white[0]=black[0]=0;

		for(int i=0;i<N;i++) {
			if(S.charAt(i)=='.') {
				white[i+1]=white[i]+1;
				black[i+1]=black[i];
			}else {
				white[i+1]=white[i];
				black[i+1]=black[i]+1;
			}
		}

		int ans=N;

		for(int i=0;i<N+1;i++) {
			int temp=(white[N]-white[i])+black[i];
			ans=Math.min(ans, temp);
		}

		System.out.println(ans);

		sc.close();
	}

}