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.io.*;
import java.util.*;

public class Main{
  public static void main(String[] args)throws IOException{
    //BufferedReader br = new BufferedReader(System.in);
    Scanner sc = new Scanner(System.in);
    PrintWriter out = new PrintWriter(System.out);
    
    int n = sc.nextInt();
		char[] s = sc.next().toCharArray();
		int b=0, w=0;
		for(int i=0;i<n;i++)
			if(s[i]=='.')
				w++;
		
		int min = w;
		for(int i=0;i<n;i++){
			if(s[i]=='#')
				b++;
			else
				w--;
 
			min = Math.min(min, w + b);
		}
		out.println(min);
    
    out.flush();
  }
}