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 boolean[] primes;

	static void primeSet(final int MAX){
		primes = new boolean[MAX+1];

		primes[2] = true;
		for(int i=3;i<=MAX;i+=2){
			primes[i] = true;
		}
		int rt = (int) Math.sqrt(MAX);
		for(int i=3;i<=rt;i+=2){
			if(primes[i]){
				for(int j=i*2;j<=MAX;j+=i){
					primes[j] = false;
				}
			}
		}
	}

	public static void main(String[] args) {
		Scanner stdIn = new Scanner(System.in);

		int max = 0;
		while(true){
			int n = stdIn.nextInt();
			if(n==0){
				break;
			}
			
			if(max<n){
				primeSet(n);
				max=n;
			}

			// if(ï) then "0" ÈóÅÍÈ¢Bn=7 ... [2,5]

			int cnt = 0;
			for(int i=2;i<=n/2;i++){
				if(primes[i]&&primes[n-i]){
//					System.out.println("["+i+","+(n-i)+"]");
					cnt++;
				}
			}
			System.out.println(cnt);
		}
	}
}