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 scanner = new Scanner(System.in);
		int N = scanner.nextInt();
		String S = scanner.next();
		scanner.close();

		char[] c = S.toCharArray();

		int[] sumBlack = new int[N+1];
		int[] sumWhite = new int[N+1];

		for (int i = 0; i < N; i++) {
			sumBlack[i+1] = sumBlack[i] + (c[i] == '#' ? 1: 0);
			sumWhite[i+1] = sumWhite[i] + (c[i] == '.' ? 1: 0);
		}

		// this code is learned by : https://atcoder.jp/contests/tenka1-2019-beginner/submissions/5069772
		// take max value of Integer 
		/*
		 * We add value to sumBlack and sumWhite, so all sumValue of each color is the time when "N".
		 * And shoule think Last time because the most right point is N.
		 */
		int min = Integer.MAX_VALUE;
		for (int j = 0; j <= N; j++) {
			// add value to sumBlack and sumWhite, so all sumValue of each color is the time when "N".
			min = Math.min(min, (sumBlack[j] + (sumWhite[N] - sumWhite[j])));
		}

		System.out.println(min);

	}

}