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 = sc.nextInt();
    String s = sc.next();
    int[] b = new int[n + 1];
    int[] w = new int[n + 1];
    int p = 0;
    for(int i = 0; i < n; i++) {
      if(s.charAt(i) == '.') p++;
    }
    w[0] = p;
    for(int i = 0; i < n; i++) {
      if(s.charAt(i) == '.') { 
        w[i + 1] = w[i] - 1;
        b[i + 1] = b[i];
      } else {
        w[i + 1] = w[i];
        b[i + 1] = b[i] + 1;
      }
    }
    int ans = n;
    for(int i = 0; i <= n; i++) {
      ans = Math.min(ans, b[i] + w[i]);
    }
    System.out.println(ans);
  }
}