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 kbd = new Scanner(System.in);
    public static void main(String[] args){
	boolean[] p = new boolean[50000];
	setp(p);
	while(kbd.hasNext()){
	    int n= kbd.nextInt();
	    if(n!=0) solve(p, n);
	}
    }

    static void solve(boolean[] p, int n){
	int ans=0, i, j;
	for(i=n-1; i>=2; i--){
	    if(p[i] && p[n-i]) {
		ans++;
		//System.out.println(i+" "+(n-i));
	    }
	}
	if(ans%2==1)
	    System.out.println(ans/2+1);
	else
	    System.out.println(ans/2);
    }

    static void setp(boolean[] p){
	Arrays.fill(p, true);
	int i, j;
	p[0] = false;
	p[1] = false;
	for(i=2; i<p.length; i++){
	    for(j=i+i; j<p.length; j+=i){
		if(p[i]) p[j] = false;
	    }
	}
    }
}