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;
	    String S;
	    
	    N=sc.nextInt();
	    S=sc.next();
	    
	    int white[]=new int[N+1];
	    int black[]=new int[N+1];
	    
	    white[0]=0;
	    black[0]=0;
	    
	    for(int i=1;i<N+1;i++){
	    	if(S.charAt(i-1)=='.') {
	    		white[i]=white[i-1]+1;
	    		black[i]=black[i-1];
	    	}else if(S.charAt(i-1)=='#') {
	    		white[i]=white[i-1];
	    		black[i]=black[i-1]+1;
	    	}
	    }
	    
	    int ans=1000000000;
	    for(int k=0;k<N+2;k++) {
	    	if(k!=N+1) {
	    	ans=ans<black[k]+(white[N]-white[k])?ans:black[k]+(white[N]-white[k]);
	    	}else {
	    	ans=ans<black[N]?ans:black[N];
	    	}
	    }
	    
	    System.out.println(ans);
	    
	}
 
}