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 N = Integer.parseInt(sc.next());
        String S = sc.next();

        int[] blackcount = new int[N];
        int bkl = 0;
        for (int i = 0; i<N; i++) {
            if (S.charAt(i)== '#') bkl++;
            blackcount[i] = bkl;
//            System.out.print(bkl);
        }
//        System.out.println();
        int blackall = blackcount[N-1];
//        System.out.println(blackall);
        int count = N;
        for (int i = 0; i < N; i++) {
            int leftchange = blackcount[i];
            int rightchange = (N-1-i-(blackall-leftchange));
            count = Math.min(count,(leftchange+rightchange));
//            System.out.println("left: " + leftchange + " right: " + rightchange + " count: " + count);
        }
        System.out.println(Math.min(count,N-blackall));
    }
}