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;

public class Main{
	public static void main(String[] args)throws IOException{
		InputStreamReader isr = new InputStreamReader(System.in);
		BufferedReader reader = new BufferedReader(isr);
		String string;
		int n, count;
		boolean[] primes = new boolean[50001];
		
		primes[0] = primes[1] = false;
		for(int i = 2; i < 50000; i++){
			boolean judge = true;
			for(int j = 2; j <= Math.sqrt(i); j++){
				if(i % j == 0){
					judge = false;
					break;
				}
			}
			if(judge) primes[i] = true;
			else      primes[i] = false;
		}
		
		while(!(string = reader.readLine()).equals("0")){
			n = Integer.parseInt(string);
			count = 0;
			
			for(int i = 0; i <= n / 2; i++){
				if(primes[i] && primes[n - i]) count++;
			}
			System.out.println(count);
		}
		reader.close();
	}
}