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 {
  final static char WHITE = '.';
  final static char BLACK = '#';

  public static void main (String[] args) {
    Scanner in = new Scanner(System.in);

    while (in.hasNext()) {
      int N = in.nextInt();
      char[] S = in.next().toCharArray();

      int[] blackBefore = new int[N];
      blackBefore[0] = 0;
      for (int i = 1; i < blackBefore.length; ++i) {
        blackBefore[i] = blackBefore[i - 1] + (S[i - 1] == BLACK ? 1 : 0);
      }

      int[] whiteAfter = new int[N];
      whiteAfter[whiteAfter.length - 1] = 0;
      for (int i = whiteAfter.length - 2; i >= 0; --i) {
        whiteAfter[i] = whiteAfter[i + 1] + (S[i + 1] == WHITE ? 1 : 0);
      }
      
      int minChange = Integer.MAX_VALUE;
      for (int i = 0; i < blackBefore.length; ++i) {
        minChange = Math.min(minChange, blackBefore[i] + whiteAfter[i]);
      }

      System.out.println(minChange);
    }
  }
}