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.Arrays;
import java.util.Scanner;

public class Main {
public static void main(String[] args) {
		
		Scanner keyboard = new Scanner(System.in); 
		
		int N = keyboard.nextInt();
		String S = keyboard.next();
		
		String[] ishi1 = S.split("");
		int count = 0;
		
		int[] Lkuro = new int[N];
		int[] Rshiro = new int[N];
		
		for (int i = 1; i < S.length(); i++) {
			if(ishi1[i-1].equals("#")) {
				Lkuro[i] = Lkuro[i-1] + 1;	
			}else {
				Lkuro[i] = Lkuro[i-1];
			}
		}
		
		for (int j = S.length() - 2; j >= 0; j--) {
			if(ishi1[j+1].equals(".")) {
				Rshiro[j] = Rshiro[j+1] + 1;	
			}else {
				Rshiro[j] = Rshiro[j+1];
			}
		}
		
		int kotae = 1000000;
		
		for(int k = 0; k < S.length(); k++) {
			kotae = Math.min(kotae, Lkuro[k]+ Rshiro[k]);
		}
		
		System.out.println(kotae);
		keyboard.close();
	}
}