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 {

	// エラトステネスのふるい(n以下の素数を求める)
	public static boolean[] sieve (int n) {
		boolean[] isPrime = new boolean[n + 1];
		Arrays.fill(isPrime, true);
		for (int i = 4; i < isPrime.length; i += 2)
			isPrime[i] = false;
		for (int i = 3; i * i <= n; i += 2) {
			for (int j = 3; i * j <= n; j += 2)
				isPrime[i * j] = false;
		}
		return isPrime;
	}

	public static int solve (int n) {
		int ret = 0;
		boolean[] primes = sieve(n);
		for (int i = 2; i <= n / 2; i++) {
			if (!primes[i]) continue;
			ret = primes[n - i] ? ret + 1 : ret;
		}
		return ret;
	}

	public static void main(String[] args) throws IOException {

		BufferedReader br =
				new BufferedReader(new InputStreamReader(System.in));

		while (true) {
			int n = Integer.parseInt(br.readLine());
			if (n == 0) break;
			System.out.println(solve(n));
		}

	}

}