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;

class Main {

  public static final long INF = Long.MAX_VALUE / 4;

  public static void main(String[] args) {
    Scanner scanner = new Scanner(System.in);
    int N = scanner.nextInt();
    String S = scanner.next();
    int[] sum = new int[N + 1];
    for (int i = 0; i < N; i++) {
      if (S.charAt(i) == '#') {
        sum[i + 1] = sum[i] + 1;
      } else {
        sum[i + 1] = sum[i];
      }
    }
    int ans = sum[N];
    for (int i = 0; i < N; i++) {
      if (S.charAt(i) == '#') {
        ans = Math.min(ans, sum[i] + N - i - 1 - (sum[N] - sum[i + 1]));
      }
    }
    System.out.println(ans);
  }
}