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.Map.Entry;
 
class Main {
	 static int mod =  (int) (Math.pow(10,9)+7);
//	 static int mod = 998244353;
	 public static void main(String[] args) {
	        Scanner sc = new Scanner(System.in);
	        int N = sc.nextInt();
	        String S = sc.next();
	        char[] c = S.toCharArray();
	        
	        int max=0;
	        int ans=3000000;
	        int bcnt=0;
	        int wcnt=0;
	        for(int i=0;i<N;i++) {
	        	if(c[i]=='#') {
		        		bcnt++;	        		
	        	} else {
		        		wcnt++;
	        	}
	        }
	        int ibcnt=0;
	        int iwcnt=0;
	        for(int i=0;i<N;i++) {
	        	ans=Math.min(ans, ibcnt+wcnt-iwcnt);
	        	if(c[i]=='#') {
	        		ibcnt++;
	        	} else {
	        		iwcnt++;
	        	}
	        }
        	ans=Math.min(ans, ibcnt+wcnt-iwcnt);
	        System.out.println(ans);
	 }
	 

}