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.Scanner;
public class Main {
	public static void main(String[] args){
		int[] prime=new int[50001];
		boolean[] primeflag=new boolean[50001];
		Scanner sc=new Scanner(System.in);
		prime[0]=2;
		primeflag[2]=true;
		prime[1]=3;
		primeflag[3]=true;
		int ptr=2;
		for(int i=5;i<=50000;i++){
			boolean flag=true;
			for(int j=0;prime[j]<=Math.sqrt(i);j++){
				if(i%prime[j]==0){
					flag=false;
				}
			}
			if(flag){
				prime[ptr++]=i;
				primeflag[i]=true;
			}
		}
		while(true){
			int n=sc.nextInt();
			if(n==0){
				break;
			}
			int count=0;
			for(int i=0;prime[i]<=n/2;i++){
				if(primeflag[(n-prime[i])]){
					count++;
				}
			}
			System.out.println(count);
		}
	}
}