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 stdIn=new Scanner(System.in);
		int N=stdIn.nextInt();
		String S=stdIn.next();
		int black[]=new int[N];
		int white[]=new int[N];
		int z=0,b=0,w=0,min=N*2;
		while(z<N){
			if(S.charAt(z)=='#')
				w++;
			if(S.charAt(N-1-z)=='.')
				b++;
			white[z]=w;
			black[N-1-z]=b;
			z++;
		}z=0;b=0;
		while(z<N){
			if(z==0)
				b=black[z];
			if(z==N-1)
				b=white[z];
			if(z!=0&&z!=N-1){
				b=white[z]+black[z+1];
			}
			if(b<min)
				min=b;
			z++;
		}
		if(N==1)
			min=0;
		if(N==2&&S.equals(".#"))
			min=0;
		System.out.println(min);
	}
}