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 static java.util.Arrays.deepToString;

import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		new Main().run();
	}
	void tr(Object... os) {
		System.err.println(deepToString(os));
	}

	Scanner sc = new Scanner(System.in);
	public void run() {
		makePrimes();
		for (;sc.hasNext();) {
			int n = sc.nextInt();
			if (n == 0) break;
			
			int res = 0;
			for (int p1: primes) {
				if (p1 < n && isPrime[n - p1] && p1 >= n - p1) {
					res++;
				}
			}
			System.out.println(res);
		}
	}
	

	static final int MAX_N = 50000 + 10;
	boolean[] isPrime = new boolean[MAX_N];
	int[] primes;
	void makePrimes(){
		if (primes != null) return;
		for (int i = 0; i < isPrime.length; i++) isPrime[i] = true;
		isPrime[0] = isPrime[1] = false;
		for (int i = 2; i * i < isPrime.length; i++)
			if (isPrime[i])
				for(int j = i * i; j < isPrime.length; j += i)
					isPrime[j] = false;
		int p = 0;
		for (int i = 2; i < isPrime.length; i++) p += isPrime[i] ? 1 : 0;
		primes = new int[p];
		p = 0;
		for (int i = 2; i < isPrime.length; i++) if (isPrime[i]) primes[p++] = i;
	}
}