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.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();	
		int [] L = new int [N+1];
		int [] R = new int [N+2];
		
		String color = sc.next(); 
		
		//count of black left of i-th tile
		int left = 0;
		for (int i=0;i<N;i++) {
			if (color.charAt(i) == '#')
				left+=1;
			L[i+1]=left;
			//System.out.println("L="+L[i]+" at i = "+i);
				
		}
		if (N!=1)
			L[N]=L[N-1];
		//System.out.println("L="+L[N]+" at i = "+N);

		//count of white tile right of i-th tile 
		int right = 0;
		for (int i=N;i>0;i--) {
			if (color.charAt(i-1) == '.')
				right+=1;
			R[i]=right;
			//System.out.println("R="+R[i]+" at i = "+i);
		}
		if (N!=1)
			R[0]=R[1];
		
		
		int tile = 100000;
		for (int i=1;i<N+1;i++) {
			//System.out.println("i="+i+" ");
			//System.out.println("L="+L[i-1]);
			//System.out.println("R="+R[i+1]);
			
			tile = Math.min(L[i-1]+R[i+1], tile);
		}
		System.out.print(tile);
	}
}