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 nWhited = 0;
        int nBlacked = 0;
        for (char s : S.toCharArray()) {
            nBlacked += s == '.' ? 1 : 0;
        }

        int nChanged = nBlacked;
        for (char s : S.toCharArray()) {
            if (s == '#') {
                nWhited += 1;
            } else {
                nBlacked -= 1;
            }

            if (nChanged > nWhited + nBlacked) {
                nChanged = nWhited + nBlacked;
            }
        }

        System.out.println(nChanged);
    }

}