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.Scanner;

public class Main {
	private Scanner sc;
	
	public static void main(String[] args) {
		new Main();
	}
	
	public Main() {
		sc = new Scanner(System.in);
		
		int[] prime = new int[50000];
		for (int i = 0; i < prime.length; i++) {
			prime[i] = 1;
		}
		
		for (int i = 2; i < (prime.length / 2); i++) {
			for (int j = 2; (i * j) < prime.length; j++) {
				prime[i * j] = 0;
			}
		}
		prime[0] = 0;
		prime[1] = 0;
		
		int num = Integer.parseInt(sc.nextLine());
		while (num != 0) {
			int sum = 0;
			for (int i = 2; i <= (num / 2); i++) {
				if ((prime[i] == 1) && (prime[num - i] == 1)) sum++;
			}
			System.out.println(sum);
			
			num = Integer.parseInt(sc.nextLine());
		}
	}
}