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.io.BufferedReader;
import java.io.InputStreamReader;

public class Main {
	public static void main(String[] args) throws Exception {

		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		String line = reader.readLine();
		int N = Integer.parseInt(line);
		String[] str = reader.readLine().split("");
		int white = 0;
		int black = 0;
		for (int j = 0; j < N; j++) {
			if (str[j].equals(".")) {
				white++;
			}
		}
		int ans = Math.min(white, N-white);   //白と黒のうち小さいほう以下
		int ans_j = 0;
		for (int j = 0; j < N; j++) {
			if (str[j].equals("#")) {
				black++;
			}
			if (str[j].equals(".")) {
				white--;
			}
			ans_j = black + white;
			if (ans > ans_j) {
				ans = ans_j;
			}
		}
		System.out.println(ans);
	}
}