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[] leftBlackCnt = new int[n];
      for(int i = 0; i < s.length(); i++) {
        if(i > 0)
          leftBlackCnt[i] = leftBlackCnt[i-1];
        if(s.charAt(i) == '#')
          leftBlackCnt[i]++;
      }

      int[] rightWhiteCnt = new int[n];
      for(int i = s.length() - 1; i >= 0; i--) {
          if(i < s.length() - 1)
            rightWhiteCnt[i] = rightWhiteCnt[i+1];
          if(s.charAt(i) == '.')
            rightWhiteCnt[i]++;
      }
      int cnt = rightWhiteCnt[0];
      for(int i = 0; i < s.length() - 1; i++) {
        cnt = Math.min(cnt, leftBlackCnt[i] + rightWhiteCnt[i+1]);
      }
      cnt = Math.min(cnt, leftBlackCnt[n-1]);
      System.out.println(cnt);
  }
}