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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;

public class Main {
	public static void main(String[] args) {

		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String line = null;

		// エラトステネスの篩
		int MAX = 50000;
		int num = (MAX - 3) / 2;
		boolean[] prime = new boolean[MAX + 1];
		Arrays.fill(prime, true);
		int[] primeArray = new int[25000];
		int count = 1;
		primeArray[0] = 2;
		
		for (int i = 0; i < num; i++) {
			if (prime[i] == true) {
				int primeNum = i + i + 3;
				primeArray[count] = primeNum;
				count++;
				for (int j = i + primeNum; j <= MAX; j += primeNum)
					prime[j] = false;
			}
		}
		
		int[] ans = new int[50001]; 
		
		for (int i = 0; primeArray[i] >= 2; i++) {
			for (int j = i; primeArray[j] >= 2 && primeArray[i] + primeArray[j] <= MAX; j++) {
				ans[primeArray[i] + primeArray[j]]++;
			}
		}

		try {
			while ((line = br.readLine()) != null) {
				line = line.trim();
				if (line.equals("0"))
					break;

				int N = Integer.parseInt(line);

				System.out.println(ans[N]);
			}
			br.close();
		} catch (IOException e) {
			e.printStackTrace();
		}
	}
}