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;

class Main{

    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int ans, n, i;
        n = sc.nextInt();
        String s = sc.next();

        int doc = 0;
        for ( i = 0; i < n; i++){
            if (s.charAt(i) == '.') doc++;
        }
        ans = doc;

        for ( i = 0; i < n; i++){
            if (s.charAt(i) == '#') doc++;
            if (s.charAt(i) == '.') doc--;
            ans = Math.min(ans,doc);
        }

        System.out.print(ans);
        sc.close();
    }
}