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.*;
import java.io.*;

public class Main {
	
	public static boolean[] sieve (int n) {
		
		boolean[] isPrime = new boolean[n];
		Arrays.fill(isPrime, true);
		
		int lim = (int)Math.sqrt(n);
		
		for (int i = 4; i < isPrime.length; i += 2)
			isPrime[i] = false;
		for (int i = 3; i <= lim; i += 2) {
			for (int j = 3; i * j < isPrime.length; j += 2)
				isPrime[i * j] = false;
		}
		
		return isPrime;
		
	}
	
	public static int solve (int n) {
		
		int cnt = 0;
		boolean[] prime = sieve(n);
		
		if (prime[n - 2]) cnt++;
		
		for (int i = 3; i <= n / 2; i += 2) {
			if (!prime[i]) continue;
			if (prime[n - i]) {
				cnt++;
			}
			
		}
		
		return cnt;
	}
	
	public static void main (String[] args) throws IOException {

		BufferedReader br =
			new BufferedReader(new InputStreamReader(System.in));
		
		while (true) {
			
			int num = Integer.parseInt(br.readLine());
			
			if (num == 0) break;
			
			System.out.println(solve(num));
			
		}
		
	}
}