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{
    final int mx = 50001;
    boolean[] prm;

    void mkPrm(){
	prm = new boolean[mx];
	for(int i = 2; i < mx; i++)
	    prm[i] = true;
	prm[0] = prm[1] = false;

	for(int i = 2; i < mx; i++)
	    if(prm[i])
		for(int j = i+i; j < mx; j += i)
		    prm[j] = false;

	return ;
    }

    Main(){
	Scanner sc = new Scanner(System.in);
	mkPrm();

	while(sc.hasNext()){
	    int n = sc.nextInt(), cnt = 0;
	    if(n == 0) break;

	    for(int i = 2; i <= n/2; i++)
		if(prm[i] && prm[n-i]) cnt++;

	    System.out.println(Integer.toString(cnt));
	}
    }

    public static void main(String[] args){
	new Main();
    }
}