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.*;
public class Main {

	public void doIt(){
		Scanner sc = new Scanner(System.in);


		//ツエツδ可トツスツテツネツスツづ個づ督づゥツつ「
		final int MAX = 50000;
		boolean [] prime = new boolean[MAX + 1];
		for(int i=2; i < prime.length; i++){
			prime[i] = true;
		}
		for(int i=2; i * i < MAX; i++){
			if(prime[i]){
				for(int j = i + i; j <= MAX; j += i){
					prime[j] = false;
				}
			}
		}

		while(true){
			int n = sc.nextInt();
			if(n == 0){
				break;
			}
			int count = 0;
			for(int i=2; i <= n/2; i++){
				if(prime[i] && prime[n-i]){
					count++;
				}
			}
			System.out.println(count);
		}

	}
	public static void main(String[] args) {
		Main obj = new Main();
		obj.doIt();

	}

}