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.*;
import java.awt.geom.*;
import java.math.*;

public class Main {

	static final Scanner in = new Scanner(System.in);
	static final PrintWriter out = new PrintWriter(System.out,false);

	static ArrayList<Integer> ps;
	static int[] cnt = new int[50001];

	static boolean solve() {
		int n = in.nextInt();
		if (n == 0) return false;

		out.println(cnt[n]);

		return true;
	}

	static ArrayList<Integer> createPrimeList(int n) {
		if (n < 2) return null;
		ArrayList<Integer> res = new ArrayList<Integer>();
		BitSet isPrimeBit = createIsPrimeBit(n);
		int p = 1;
		while ((p = isPrimeBit.nextSetBit(p+1)) >= 0) {
			res.add(p);
		}
		return res;
	}

	static BitSet createIsPrimeBit(int n) {
		if (n < 2) return null;
		BitSet res = new BitSet();
		res.set(2,n,true);
		for (int i=2; i*i<n; i=res.nextSetBit(i+1)) {
			for (int j=i+i; j<n; j+=i) res.set(j,false);
		}
		return res;
	}

	public static void main(String[] args) {
		long start = System.currentTimeMillis();

		ps = createPrimeList(50000);

		for (int px : ps) {
			for (int py : ps) {
				if (px > py) continue;
				if (px + py <= 50000) cnt[px+py]++;
			}
		}

		while(solve());
		out.flush();

		long end = System.currentTimeMillis();
		//trace(end-start + "ms");
		in.close();
		out.close();
	}

	static void trace(Object... o) { System.out.println(Arrays.deepToString(o));}
}