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.*;
 class Main {
    public static void main(String[] args) {
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        String s=sc.next();
        int w=0;
        int b=0;
        int a=0;
        for(int i=0;i<n;i++)
        {
            if(s.charAt(i)=='.')
                w++;
        }
        a=w;
        for(int i=0;i<n;i++)
        {
            if(s.charAt(i)=='#')
                b++;
            else
                w--;
            a=Math.min(a, (w+b));
        }
        
        System.out.println(a);
    }
}