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.Arrays;
import java.util.Scanner;

public class Main
{
	public static void main(String arg[])
	{
		Scanner sc = new Scanner(System.in);

		boolean a[] = new boolean [50001];
		Arrays.fill(a, true);
		a[0]=a[1]=false;
		for(int i=0; i*i<=50000;i++)
		{
			if(!a[i])
				continue;
			for(int j=i*2; j<=50000; j+=i)
				a[j]=false;
		}

		while(sc.hasNext())
		{
			int n=sc.nextInt();
			if(n==0)
				return;
			int ans=0;

			for(int i=1; i<=n/2; i++)
			{
				if(!a[i])
					continue;
				if(a[n-i])
				{
					//System.out.println(i+" "+(n-i));
					ans++;
				}
			}
			System.out.println(ans);

		}
	}

}