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 boolean[] p=new boolean[50000];
	public static int counter(int n){
		int c=0,i,j;
		for(i=2;i<=n/2;i++){
			if(p[i]&&p[n-i]) c++;
//			for(j=2;i+j<=n;j++){
//				if(p[j]){
//					if(i+j==n){
//						c++;
////						System.out.println(i+" "+j);
//					}
//				}
//			}//
		}//
		return c;
	}
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		int n,i,j;
		Arrays.fill(p, true);
		for(i=2;i<50000;i++){
			if(p[i])
			for(j=2;i*j<50000;j++){
				p[i*j]=false;
			}
		}
		while(true){
			n=sc.nextInt();
			if(n==0) break;
			System.out.println(counter(n));
		}
	}
}