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();
	sc.close();
	int bl =0; int wh =0;
	for(int i =0; i<n; i++) {
     if(s.charAt(i)=='.') {
    	 wh++;
     }
}
	int min = wh;
	for(int i =0; i<n; i++) {
	     if(s.charAt(i)=='#') {
	    	 bl++;
	     }
	     else {
	    	 wh--;
	     }
	     min = Math.min(min, wh+bl);
	}
	
  System.out.println(min);
    }

}