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{
	public static void main(String[] args){
		Scanner scan = new Scanner(System.in);
		int[] v = new int[25000];
        for(int i = 0;i < 25000;i++){
            v[i] = 1;
        }
        int p = 3;
        while(true){
            if(p*p > 50000){
                break;
            }else{
                if(v[(p-1)/2] == 0){
                    p += 2;
                }else{
                    int t = p*p;
                    while(t < 50000){
                        v[(t-1)/2] = 0;
                        t += 2*p;
                    }
                    p += 2;
                }
            }
        }
		while(scan.hasNext()){
			int n = scan.nextInt();
			if(n == 0){
				break;
			}else if(n == 4){
				System.out.println(1);
				continue;
			}else if(n%2 != 0){
				if(v[(n-3)/2] == 1){
					System.out.println(1);
				}else{
					System.out.println(0);
				}
				continue;
			}
			int count = 0;
			for(int i = 1;i <= (n/2-1)/2;i++){
				if(v[i] == 1 && v[n/2-i-1] == 1){
					count++;
				}
			}
			System.out.println(count);
		}
	}
}