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 answer;
		int[] table = new int[50001];
		table[0] = 0;
		table[1] = 0;
		for (int i = 2; i <= 50000; i++) {
			table[i] = 1;
		}
		for (int i = 2; i <= Math.sqrt(50000) + 1; i++)
			if (table[i] == 1)
				for (int j = i * 2; j <= 50000; j += i)
					table[j] = 0;
		while (true) {
			int n = sc.nextInt();
			answer = 0;
			if (n == 0)
				break;
			if (n >= 4) {
				for (int i = 2; i <= n / 2; i++)
					if (table[i] == 1 && table[n - i] == 1)
						answer++;
			}
			System.out.println(answer);
		}
		sc.close();
	}
}