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.*;
import java.io.ObjectInputStream.*;
import java.util.*;
import java.util.regex.*;


public class Main {

	final static long MOD = 1000000007;
	//final static long MOD = 998244353;

	public static String[] Ws = null;
	public static int wsIndx = 0;
	public static BufferedReader in = null;
	public static long cnt=0;
	public static PrintWriter pw = new PrintWriter(System.out);
	public static void main(String[] args) throws Exception {
		solutionA(args);
		if(in!=null){
			in.close();
		}
		pw.flush();
		pw.close();
	}

	public static void solutionA(String[] args) throws Exception{
		int N = nextInt();
		char[] s = nextString().toCharArray();

		int rb=0;
		int rw=0;
		for(int i=0;i<N;i++) {
			if(s[i]=='#') {
				rb++;
			}else {
				rw++;
			}
		}

		int lb=0;
		int lw=0;
		int ans =Math.min(rb,rw);
		for(int i=0;i<N;i++) {
			if(s[i]=='.') {
				lw++;
				rw--;
			}else {
				lb++;
				rb--;
			}
			ans=Math.min(ans,lb+rw);
		}

		pw.println(ans);

	}


	public static void check() throws Exception{
		if(in == null){
			in = new BufferedReader(new InputStreamReader(System.in));
		}
		if(Ws==null || Ws.length<=wsIndx){
			Ws = in.readLine().split(" ");
			wsIndx=0;
		}
	}
	public static int nextInt()throws Exception{
		check();
		return Integer.parseInt(Ws[wsIndx++]);
	}

	public static long nextLong()throws Exception{
		check();
		return Long.parseLong(Ws[wsIndx++]);
	}

	public static String nextString()throws Exception{
		check();
		return Ws[wsIndx++];
	}

	public static int[] nextInts()throws Exception{
		check();
		int[] tmp = new int[Ws.length];
		for(int i=0;i<tmp.length;i++){
			tmp[i]=Integer.parseInt(Ws[i]);
		}
		wsIndx=Ws.length;
		return tmp;
	}

	public static long[] nextLongs()throws Exception{
		check();
		long[] tmp = new long[Ws.length];
		for(int i=0;i<tmp.length;i++){
			tmp[i]=Long.parseLong(Ws[i]);
		}
		wsIndx=Ws.length;
		return tmp;
	}

	public static String[] nextStrings()throws Exception{
		check();
		wsIndx=Ws.length;
		return Ws;
	}


}