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();
		char[] S = sc.next().toCharArray();
		int[] bl = new int[N+1];
		for(int i = 1; i <= N; i++) {
			bl[i] = bl[i-1];
			if(S[i-1] == '#')
				bl[i]++;
		}
		int ans = Math.min(N - bl[N], bl[N]);
		for(int i = 1; i <= N; i++) {
			int black = bl[N]-bl[i];
			int white = N-bl[N]-(i-bl[i]);
			if(black > white) {
				ans = Math.min(ans, bl[i] + white);
			}
		}
		System.out.println(ans);

	}

}