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.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;

public class Main {
	static int N;
	static String S;
	static int[] sum;

	public static void main(String[] args) {
		//入力
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		try {
			N = Integer.parseInt(br.readLine());
			S = br.readLine();
			sum = new int[N+1];
		} catch(IOException e) {
			e.printStackTrace();
		}

		for(int i=0; i<N; i++) {
			if(S.charAt(i)=='.') sum[0]++;
		}

		for(int i=1; i<N+1; i++) {
			if(S.charAt(i-1)=='#') {
				sum[i] = sum[i-1] + 1;
			} else {
				sum[i] = sum[i-1] - 1;
			}
		}

		Arrays.sort(sum);
		System.out.println(sum[0]);
	}
}