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 num = sc.nextInt();
		String s = sc.next();
		String[] line = s.split("");
        List<Integer> array = new ArrayList<Integer>();
        int count = 0;
		//int sum = 0;
		int min = num;
for(int i=0; i<num; i++){
  if(line[i].equals(".")) count++;
}
int sum = count;
for(int i=0; i<num; i++){
  if(sum < min) min = sum;
  if(line[i].equals("#")) sum++;
  else sum--;
  //System.out.println(sum);
}
if(sum < min) min = sum;
System.out.println(min);
    }
}