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 sc = new Scanner(System.in);
		int n = sc.nextInt();
		String s = sc.next();
		int whitecnt = 0;
		for(int i = 0;i < n;i ++) {
			char c = s.charAt(i);
			if(c == '.') whitecnt ++; //一旦全部黒にすることを考える
		}
		int cntmin = whitecnt, cnt = whitecnt;
		//前から徐々に白にする
		for(int i = 0;i < n;i ++) {
			char c = s.charAt(i);
			if(c == '.') cnt--; //黒にしてあったところ分のカウントを無くす
			else cnt++; //黒を白にする
			cntmin = Math.min(cnt, cntmin);
		}
		System.out.println(cntmin);
	}
}