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;
import java.util.Vector;

public class Main {
	public static void main(String[] args) {
		int[] p = new int[50000+1];
		p[0] = p[1] = 0;
		for(int i = 2; i <= 50000; i++) {
			p[i] = 1;
		}
		for(int i = 2; i <= Math.sqrt(50000)+1; i++) {
			if(p[i] == 1) {
				for(int j = i*2; j <= 50000; j+=i) {
					p[j] = 0;
				}
			}
		}
		
		Scanner sc = new Scanner(System.in);
		while(true) {
			int n = sc.nextInt();
			if(n == 0) {
				break;
			}
			int ans = 0;
			for(int i = 2; i <= n/2; i++) {
				if(p[i] == 1 && p[n-i] == 1) {
					ans++;
				}
			}
			System.out.println(ans);
		}
	}
}