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();

		char c[]=new char[n];
		int blackcount=0;
		int blacknum=0;
		int min=n;

		for(int i=0;i<n;++i){
			if(s.charAt(i)=='#')++blacknum;

		}
		for(int i=0;i<n;++i){
			if(s.charAt(i)=='#'){
				++blackcount;
				min=Math.min(min, blackcount-1+(n-1-i)-blacknum+blackcount);
			}
			else min=Math.min(min, blackcount+(n-1-i)-blacknum+blackcount);
		}

		System.out.println(min);


	}
}