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.*;

class Main{
  public static void main(String[] args){
    Scanner sc=new Scanner(System.in);
    int n=sc.nextInt();
    String s=sc.next();
    int[] wb=new int[n+1];
    int[] ww=new int[n+1];
    for(int i=0;i<n;i++){
      wb[i+1]=wb[i];
      ww[i+1]=ww[i];
      (s.charAt(i)=='#'?wb:ww)[i+1]++;
    }
    int min=n;
    for(int i=0;i<=n;i++){
      min=Math.min(wb[i]-wb[0]+ww[n]-ww[i],min);
      //System.err.println((wb[i]-wb[0])+" : "+(ww[n]-ww[i]));
    }
    System.out.println(min);
  }
}