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 {
	static boolean isPrime[] = new boolean[50001];
    public static void main(String[] args){
    	Scanner input = new Scanner(System.in);
    	for(int i = 1 ; i <= 50000 ; i++){
    		isPrime[i] = isPrime(i);
    	}
    	while(input.hasNext()){
    		int a = input.nextInt();
    		if(a == 0)break;
    		System.out.println(gold(a));
    	}
    }
    
    public static int gold(int a){
    	int count = 0;
    	for(int i = 2 ; i <= a/2 ; i++){
    		if(isPrime[i] && isPrime[a-i])count++;
    	}
    	return count;
    }
    
    public static boolean isPrime(int n){
    	if(n == 2)return true;
    	if(n % 2 == 0)return false;
    	for(int i = 3 ; i <= Math.sqrt(n) ; i++){
    		if(n % i == 0)return false;
    	}
    	return true;
    }
}