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.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.IOException;

public class Main {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        int n = Integer.parseInt(br.readLine());
        char[] s = br.readLine().toCharArray();
        
        int[] black = new int[n + 1];
        int[] white = new int[n + 1];
        for(int i = 0; i < n; i++) {
            if(s[i] == '#') {
                black[i + 1] = black[i] + 1;
                white[i + 1] = white[i];
            }else {
                black[i + 1] = black[i];
                white[i + 1] = white[i] + 1;
            }
        }

        int ans = 1000000;
        for(int i = 0; i <= n; i++) {
            ans = Math.min(ans, black[i] + white[n] - white[i]);
        }
        System.out.println(ans);

        br.close();
    }
}