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.io.InputStream;
import java.io.PrintStream;
import java.util.*;

public class Main {

  public static void main(String[] args) {
    solve(System.in, System.out);
  }

  static void solve(InputStream is, PrintStream os) {
    Scanner sc = new Scanner(is);

    /* read */
    int n = sc.nextInt();
    String s = sc.next();
    boolean[] b = new boolean[n];

    for (int i = 0 ; i < n; i++) {
      if (s.charAt(i) == '#') { // black
        b[i] = false;
      } else { // white
        b[i] = true;
      }
    }

    /* logic */

    // first target is all false.
    int count = 0;
    for (int i = 0; i < n; i++){
      if (b[i]) {
        count++;
      }
    }
    
    int answer = count;
    for (int i = 0; i < n; i++){
      // target is [0..i] is true, [i + 1..n - 1]  is false
      // i index should be true
      if (!b[i]) {
        count++;
      } else {
        count--;
      }
      answer = Math.min(answer, count);
    }
    os.print(answer);

  }
}