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 sc = new Scanner(System.in);
    int N = Integer.parseInt(sc.nextLine());
    String S = sc.nextLine();
    int w = 0, b = 0;
    for(int i = 0; i < N; i++){
      if(S.charAt(i) == '.'){
        w++;
      }
    }
    
    int ans = w;
    for(int i = 0; i < N; i++){
      if(S.charAt(i) == '#'){
        b++;
      }else{
        w--;
      }
      ans = Math.min(ans, b+w);
    }
    System.out.println(ans);
  }
}