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.*;
import java.util.regex.Pattern;

public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		String S = sc.next();

		String[] s = S.split("");

		int[] bCnt = new int[N+1];
		bCnt[0] = 0;

		for(int i=1; i<N+1; i++){
			if(s[i-1].equals("#")){
				bCnt[i] = bCnt[i-1]+1;
			} else{
				bCnt[i] = bCnt[i-1];
			}
		}

		int[] wCnt = new int[N+1];
		wCnt[N]=0;

		for(int i=N-1; i>-1; i--){
			if(s[i].equals(".")){
				wCnt[i]= wCnt[i+1]+1;
			}else{
				wCnt[i]= wCnt[i+1];
			}
		}

		int min = 200001;

		for(int i=0; i<N+1; i++){
			if(min>bCnt[i]+wCnt[i]){
				min = bCnt[i]+wCnt[i];
			}
		}

		System.out.println(min);


	}


}