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 = sc.nextInt();
        String s = sc.next();
        int[] blackSum = new int[n+1];
        for(int i = 0; i < n; i++) {
            if(s.charAt(i) == '#') blackSum[i+1] = blackSum[i] + 1;
            else blackSum[i+1] = blackSum[i];
        }
        int min = n;
        for(int i = 0; i < n+1; i++) {
            int rightBlack = blackSum[i] - blackSum[0];
            int leftBlack = blackSum[n] - blackSum[i];
            int leftWhite = n - i - leftBlack;
            min = Math.min(min, rightBlack+ leftWhite);
        }
        System.out.println(min);
    }
}