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.*;
import java.io.*;

public class Main{
	public static void main(String[] args){
		Scanner stdIn = new Scanner(System.in);
		List<Integer> prime = new ArrayList<Integer>();
		prime.add(2); prime.add(3);
		int[] check = new int[50001];
		check[2] = 1; check[3] = 1;
		
	outer:	for(int i = 5; i < 50000; i += 2){
			for(int j = 1; prime.get(j) <= Math.sqrt(i); j++){
				if( i%prime.get(j) == 0 ){
					continue outer;
				}
			}
			prime.add(i);
			check[i] = 1;			
		}
		
		List<Integer> result = new ArrayList<Integer>();
		int n = stdIn.nextInt();
		while( n != 0 ){
			if( n%2 != 0 ){
				if( check[n-2] == 1 ){
					result.add(1);
				} else {
					result.add(0);
				}
			
			} else {
				int sum = 0;
				int index = 0;
				while( prime.get(index) <= n/2 ){
					if( check[n-prime.get(index)] == 1 ){
						sum++;
					}
					index++;
				}
				result.add(sum);
			}
			n = stdIn.nextInt();
		}
		for(Integer sum : result){
			System.out.println(sum);
		}
	}
}