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[] w = new int[n+1];
    int[] b = new int[n+1];
    for(int i = 1;i <= n;i++){
      if(s.charAt(i-1)=='.'){
        w[i]=w[i-1]+1;
        b[i]=b[i-1];
      }else{
        w[i]=w[i-1];
        b[i]=b[i-1]+1;
      }
    }
    int min = 1000000000;
    for(int i = 0;i <= n;i++){
      min = Math.min(min,b[i]+w[n]-w[i]);
    }
    System.out.println(min);
  }
}