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.*;
public class Main{
    public static void main(String[] args) throws IOException{
        BufferedReader bf = 
            new BufferedReader(new InputStreamReader(System.in));
        int N = Integer.parseInt(bf.readLine());
        String S = bf.readLine();
        int min;
        int count = 0;
        for(int i = 0; i < N; i++){
            if(S.charAt(i) == '.'){
                count++;
            }
        }
        min = count;
        for(int i = 0; i < N && 0 < min; i++){
            if(S.charAt(i) == '#'){
                count++;
            } else{
                count--;
                if(count < min){
                    min = count;
                }
            }            
        }           
        System.out.println(min);
    }
}