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.ArrayList;
import java.util.Scanner;


public class Main
{
	static ArrayList<Integer> prime = new ArrayList<>();
	
	public static void main(String[] args)
	{
		Scanner scanner = new Scanner(System.in);
		
		create();
		
		for(; ;)
		{
			int count = 0;
			int n = scanner.nextInt();
			if(n == 0)
			{
				break;
			}			
            for(int i=0; i<prime.size(); i++)
            {
            	int num = n-prime.get(i);
            	if(num == prime.get(i))
            	{
            		count ++;
            	}
            	else if (num > prime.get(i)) 
            	{				
            		if(isPrime(num))
            		{
            			count ++;
            		}
            	}
            	else
            	{
            		break;
            	}
            }
            System.out.println(count);
		}
	}
	
	static void create()
	{
		for(int i=2; i<=50000; i+=(i==2)?1:2)
		{
			if(isPrime(i))
			{
				prime.add(i);
			}	
		}
	}
	
	static boolean isPrime(int n)
	{
		int p = (int)Math.sqrt(n);
		boolean is_prime = true;
		for(int i=2; i<=p; i+=(i==2)?1:2)
		{
			if(n % i == 0)
			{
				is_prime = false;
				break;
			}
		}
		return is_prime;
	}
}