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 {

	static final int MAX = 50000;
	static boolean[] era = new boolean[MAX+1];
	static{
		era[0]=era[1]=true;
		for (int i = 2; i*i <= MAX ; i++) {
			if(!era[i]) for (int j = i*2; j <=MAX ; j+=i) {
				era[j]=true;
			}
		}
	}


	public static void main(String[] args) {

		Scanner scan = new Scanner(System.in);

		int n;
		while((n=scan.nextInt())!=0){
			int k=0;
			for (int i = 2; i <=n/2 ; i++) {
				if(n-i<0) break;
				if(!era[i] && !era[n-i]) k++;
			}
			System.out.println(k);
		}
	}
}