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;

class Main
{
	public static void main(String args[])
	{
		boolean not[] = new boolean[100000];
		not[0] = true;
		not[1] = true;
		int pCount = 2;
		for (int i = 2; i * i < 100000; i++)
		{
			if (not[i]) continue;
			for (int x = (i << 1); x < 100000; x += i)
			{
				if (not[x]) continue;
				not[x] = true;
				pCount++;
			}
		}
		int primes[] = new int[100000 - pCount];
		int index = 0;
		for (int i = 0; i < 100000; i++)
		{
			if (!not[i])
			{
				primes[index] = i;
				index++;
			}
		}
		Scanner sc = new Scanner(System.in);
		while (true)
		{
			int n = sc.nextInt();
			if (n == 0) break;
			int count = 0;
			int m = n / 2 + 1;
			for (int i = 0; primes[i] < m; i++)
			{
				if (not[n - primes[i]]) continue;
				count++;
			}
			System.out.println(count);
		}
	}
}