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.Scanner;

public class Main {

	Scanner sc;
	int[] table = new int[ 50001 ];
	int[] prime = new int[ 50001 ];
	int pCounter = 0;

	private Main(){
		sc = new Scanner( System.in );
		table[ 1 ] = 1;
		for( int i = 2; i < table.length; i++ ){
			table[ i ] = 0;
		}
		for( int i = 2; i < table.length; i++ ){
			if( table[ i ] == 1 ){ continue; }
			prime[ pCounter++ ] = i;
			for( int j = i * 2; j < table.length; j += i){
				table[ j ] = 1;
			}
		}
	}

	private void run(){
		while( true ){
			int n = sc.nextInt();
			if( n == 0 ){ break; }
			int counter = 0;

			for( int i = 0; prime[ i ] <= n / 2; i++ ){
				int cN = n - prime[ i ];
				if( table[ cN ] == 0 ){ counter++; }
			}
			System.out.println( counter );
		}
	}
	public static void main( String[] args ){
		new Main().run();
	}
}