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.math.*;

class Main{
    
    public static void main(String[] args){
        Scanner in = new Scanner(System.in);
        
        int n = in.nextInt();
        String s = in.next();
        
        int doc = 0;
        for (int i = 0; i < s.length(); ++i){
            if (s.charAt(i) == '.') ++doc;
        }
        int ans = doc;
        
        for (int i = 0; i < s.length(); ++i){
            if (s.charAt(i) == '#') ++doc;
            if (s.charAt(i) == '.') --doc;
            ans = Math.min(ans,doc);
        }
        
        System.out.print(ans);
    }
}