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.io.*;
import java.util.*;

class Main{
    public static void main(String[] args){
	BufferedReader sc=new BufferedReader(new InputStreamReader(System.in));
	try{
	    boolean[] prime = new boolean[50000];
	    Arrays.fill(prime, true);
	    prime[1]=prime[0]=false;
	    for(int i=2; i<Math.sqrt(50000); i++)
		if(prime[i])
		    for(int j=i*i; j<50000; j+=i)
			prime[j]=false;
	    int n, count;
	    while((n = Integer.valueOf(sc.readLine()))!=0){
		if(n%2==1)
		    if(prime[n-2])
			System.out.println(1);
		    else
			System.out.println(0);
		else{
		    count = 0;
		    for(int i=2; i<=n/2; i++)
			if(prime[i]&&prime[n-i])
			    count++;
		    System.out.println(count);
		}
	    }
    	}catch (Exception e){
	    System.out.println("Error");
	}
    }
}