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(final String[] args) {

        try (final Scanner sc = new Scanner(System.in)) {
            int N = sc.nextInt();
            String S = sc.next();
            // 累積和つくる
            int[] bSum = new int[N + 1];
            int[] wSum = new int[N + 1];
            for (int i = 0; i < N; i++) {
                char c = S.charAt(i);
                bSum[i + 1] = bSum[i] + (c == '#' ? 1 : 0);
                wSum[i + 1] = wSum[i] + (c == '.' ? 1 : 0);
            }
            // 各位置における（左の黒の数＋右の白の数）を求めて、そのうち一番小さいものを採用する
            int min = Integer.MAX_VALUE;
            for (int i = 0; i <= N; i++) {
                int leftB = bSum[i];
                int rightW = wSum[N] - wSum[i];
                min = Math.min(min, leftB + rightW);
            }
            System.out.println(min);
        }
    }

}