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) throws IOException {

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

		boolean[] primes = new boolean[50001];
		Arrays.fill(primes, true);

		for (int i = 2; i < 50001; i++) {
			if (primes[i]) {
				for (int j = 2; j <= 50000 / i; j++) {
					primes[i * j] = false;
				}
			}
		}

		while (!(line = br.readLine()).equals("0")) {

			int n = Integer.parseInt(line);
			int c = 0;

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

	}

}