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.*;
 
public class Main{
	public static void main(String[] args){
    	Scanner scan = new Scanner(System.in);
      	int N = scan.nextInt();
      	String s = scan.next();
      	int counterW = 0;
      	for(int i = 0; i < N; i++){
        	if(s.substring(i, i+1).contains(".")){
            	counterW++;
            }
        }
        int pointer = counterW;
      	int ans = counterW;
      	for(int i =0; i < N; i++){
        	if(s.substring(i, i+1).contains(".")){
            	pointer--;
            }
          	else{
            	pointer++;
            }
          	ans = Math.min(ans, pointer);
        }
      	System.out.print(ans);
    }
 
}