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 {
	public static void main(String args[]) {
		Scanner sc = new Scanner(System.in);
		int prime[] = new int[50000];
		int n;
		int count;
		
		for (int i = 2; i < 50000; i++) {
			for (int j = i; j < 50000; j++) {
				if (0 <= i * j && i * j < 50000) {
					prime[i * j] = 1;
				} else {
					break;
				}
			}
		}
		n = sc.nextInt();
		while (n != 0) {
			count = 0;
			for (int i = 2; i <= n / 2; i++) {
				if (prime[i] == 0 && prime[n - i] == 0) {
					count++;
				}
			}
			System.out.println(count);
			n = sc.nextInt();
		}
	}
}