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();
        sc.close();
        
        int white = 0;
        int black = 0;
        int[] color = new int[N];
        String[] text = new String[N];

        for (int i = 0; i < N; i++) {
            text[i] = String.valueOf(S.charAt(i));
            if(i != 0 && text[i].equals("#")){
                black++;
                color[i] = color[i-1]+1;
            }else if(i == 0 && text[i].equals("#")){
                black++;
                color[i] = 1;
            }else if(i == 0 && text[i].equals(".")){
                white++;
                color[i] = 0;
            }else{
                white++;
                color[i] = color[i-1];
            }


            //System.out.println(color[i]);
        }

        //System.out.println(black);
        //System.out.println(white);


        int ans = 300000;
        int tmp= 0;
        for (int i = 0; i < N; i++) {
                int bb = color[i];
                int ww = (N-i-1) - (color[N-1] - color[i]);
                //System.out.println(bb);
                //System.out.println(ww);
                tmp = bb+ww;
                //System.out.println(tmp);

                if(ans > tmp){
                    ans = tmp;
                }
        }

        if(white == 0 || black == 0){
            System.out.println("0");
        }
        else if(N-color[N-1] < ans){
            System.out.println(N-color[N-1]);
        }
        else{
            System.out.println(ans);
        }

    }
}