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.*;

class Main {
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int n = Integer.parseInt(sc.next());
    String s = sc.next();

    String check = "";
    int todot = 0;
    int current;
    int min;

    for (int i=0; i<n; i++) {
      check = s.substring(i,i+1);
      if (check.equals(".")) {
        todot++;
      }
    }
    
    current = todot;
    min = todot;
    
	for (int i=0; i<n; i++) {
      check = s.substring(i,i+1);
      if (check.equals(".")) {
        current--;
      } else {
        current++;
      }
      if (current < min) {
        min = current;
      }
    }
    
    System.out.println(min);
  }
}