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.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();
        char[] s = sc.next().toCharArray();

        int[] black = new int[n];
        for (int i = 1; i < n; i++) {
            black[i] = black[i-1] + (s[i-1] == '#' ? 1 : 0);
        }
        
        int[] white = new int[n];
        for (int i = n-2; i >= 0; i--) {
            white[i] = white[i+1] + (s[i+1] == '.' ? 1 : 0);
        }
        
        int min = Integer.MAX_VALUE;
        for (int i = 0; i < n; i++) {
            min = Math.min(min, black[i] + white[i]);
        }
        
        System.out.println(min);
    }
}