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.*;
public class Main {
	static Scanner sc = new Scanner(System.in);
	static boolean[] prime = new boolean[50001];
	static int n;
	public static void main(String[] args) {
		make_prime();
		while(read()){
			solve();
		}
	}
	
	static boolean read(){
		n = sc.nextInt();
		if(n == 0)return false;
		return true;
	}
	
	static void solve(){
		int res = 0;
		for(int i = 2; i <= n/2; i++){
			if(prime[i] && prime[n - i]){
				res++;
			}
		}
		System.out.println(res);
	}
	
	static void make_prime(){
		Arrays.fill(prime, true);
		prime[0] = false;
		prime[1] = false;
		for(int i = 2; i < prime.length; i++){
			if(prime[i]){
				for(int j = 2*i; j < prime.length; j += i){
					prime[j] = false;
				}
			}
		}
	}

}