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 n = scan.nextInt();
	String s = scan.next();

	//初期のドットの数
	int firstDot = 0;
	for(int i = 0; i < n; i++){
	    if(s.charAt(i) == '.'){
		firstDot++;
	    }
	}

	int min = firstDot;
	int tmp = firstDot;
	//基準を設定
	//基準より左は .
	//基準より右は #
	for(int i = 0; i < n; i++){
	    //変える必要がない .
	    if(s.charAt(i) == '.'){
		tmp--;
		//変える必要がある#
	    }else{
		tmp++;
	    }
	    if(min > tmp){
		min = tmp;
	    }
	}

	System.out.println(min);
    }
}