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.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner();
		int n = sc.nextInt();
		String s = "." + sc.next();
		int sum = 0;
		for(int i = 1; i < s.length(); i++) 
			if(s.charAt(i) == '.')
				sum++;
		
		long min = sum;
		for(int i = 1; i < s.length(); i++) {
			int val = sum;
			if(s.charAt(i) == '#')
				val++;
			else
				val--;
			if(min > val)
				min = val;
			sum = val;
		}
		
		System.out.println(min);
		
	}
}

class Scanner {
	private static final int SPACE = (int)' ';
	private static final int LINE_END_0 = 13;
	private static final int LINE_END_1 = 10;
	private static final int BEFORE = -1;
	private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	
	public String next(){
		StringBuilder sb = new StringBuilder();
		
		int length = BEFORE;
		readLoop: while(true) {
			try {
				int value = br.read();
				switch(value) {
				case LINE_END_1:
					if(length == BEFORE)
						break;
					
					if((int)sb.charAt(length) == LINE_END_0)
						sb.deleteCharAt(length);
				case SPACE:
					break readLoop;
				}
				sb.append((char)value);
				length++;

			} catch (IOException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
		}
		return sb.toString();
	}
	
	public String[] nextArray(int length) {
		String[] array = new String[length];
		for(int i = 0; i < length; i++)
			array[i] = next();
		return array;
	}
	
	public double nextDouble() {
		return Double.parseDouble(next());
	}
	
	public double[] nextDoubleArray(int length) {
		double[] array = new double[length];
		for(int i = 0; i < length; i++)
			array[i] = nextDouble();
		return array;
	}
	
	public int nextInt() {
		return Integer.parseInt(next());
	}
	
	public int[] nextIntArray(int length) {
		int[] array = new int[length];
		for(int i = 0; i < length; i++)
			array[i] = nextInt();
		return array;
	}
	
	public long nextLong() {
		return Long.parseLong(next());
	}
	
	public long[] nextLongArray(int length) {
		long[] array = new long[length];
		for(int i = 0; i < length; i++)
			array[i] = nextLong();
		return array;
	}
	
	public boolean ready() {
		try {
			return br.ready();
		} catch (IOException e) {
			// TODO Auto-generated catch block
			e.printStackTrace();
		}
		return false;
	}
}