It is known that even numbers greater than or equal to 4 can be represented by the sum of two prime numbers. This is called the Goldbach's conjecture, and computer calculations have confirmed that it is correct up to a fairly large number. For example, 10 can be represented by the sum of two prime numbers, 7 + 3 and 5 + 5.

Write a program that inputs the integer n and outputs how many combinations of n are the sum of two prime numbers. However, n must be 4 or more and 50,000 or less. Also, the n entered is not always even.



Input

Given multiple datasets. Each dataset is given n on one row. When n is 0, it is the last input. The number of datasets does not exceed 10,000.

Output

For each dataset, output the number of combinations in which n is the sum of two prime numbers on one line.

Example

Input

10
11
0


Output

2
0
import java.util.Arrays;
import java.util.Scanner;

//Goldbach's Conjecture
public class Main{

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		boolean[] p = new boolean[50001];
		Arrays.fill(p, true);
		p[0] = p[1] = false;
		for(int i=2;i<50001;i++)if(p[i])for(int j=i*2;j<50001;j+=i)p[j]=false;
		while(true){
			int n = sc.nextInt();
			if(n==0)break;
			int c = 0;
			for(int i=2;i<=n/2;i++)if(p[i]&&p[n-i])c++;
			System.out.println(c);
		}
	}
}