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 {
  static char[] colors = {'.', '#'};

  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    String s = sc.next();
    Main tenkaC = new Main();
    System.out.println(tenkaC.solve(n, s));
  }

  public int solve(int n, String s) {
    int whiteNum = 0;
    int blackNum = 0;
    int[] whiteNums = new int[n];
    int[] blackNums = new int[n];
    for(int i = 0; i< n; i++ ){
      if(s.charAt(i) == '.' ){
        whiteNum += 1;
      } else {
        blackNum += 1;
      }
      whiteNums[i] = whiteNum;
      blackNums[i] = blackNum;
    }
    int ans = whiteNum;
    for(int i = 0; i < n; i++ ){
      ans = Math.min(ans, blackNums[i] + whiteNum - whiteNums[i]);
    }
    return ans;
  }
}