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.io.*;
import java.nio.charset.StandardCharsets;

public class Main {
	int N;
	String S;
	int[] lefts, rights;
	int result = Integer.MAX_VALUE;
	
	Main() throws IOException {
		InputStreamReader reader = new InputStreamReader(System.in, StandardCharsets.UTF_8);
		BufferedReader in = new BufferedReader(reader);
		N = Integer.parseInt(in.readLine());
		S = in.readLine();
		in.close();
		this.lefts = new int[2];
		this.rights = new int[2];
		init();
		calc();
	}
	
	void init() {
		this.lefts[0] = 0;
		this.lefts[1] = 0;
		this.rights[0] = 0;
		this.rights[1] = 0;
		for(int i = 0; i < S.length(); ++i) {
			if(S.charAt(i) == '#') {
				++rights[1];
			}else {
				++rights[0];
			}
		}
	}

	void calc() {
		this.result = this.rights[0];
		for(int i = 0; i < S.length(); ++i) {
			if(S.charAt(i) == '#') {
				--rights[1];
				++lefts[1];
			}else {
				--rights[0];
				++lefts[0];
			}
			this.result = Math.min(result, rights[0] + lefts[1]);
		}
	}

	public static void main(String[] args) throws IOException {
		Main ins = new Main();
		System.out.println(ins.result);

	}

}