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.Arrays;
import java.util.Scanner;


public class Main {
	
	boolean[] getPrime(final int n){
		boolean[] list = new boolean[n+1];
		for(int i=2; i<=n; ++i){ list[i] = true;}
		for(int i=2; i*i<=n; ++i){
			if(list[i]){
				for(int j=i*2; j<=n; j+=i){
					list[j] = false;
				}
			}
		}
		return list;
	}
	
	int countGoldbach(final boolean[] map){
		int c=0;
		int target = map.length -1;
		
		for(int i=2; i<=target/2; ++i){
			int j = target - i;
			if(map[i] && map[j])++c;
		}
		
		return c;
	}
	
	void io(){
		Scanner sc = new Scanner(System.in);
		for(;;){
			final int n = sc.nextInt();
			if(n==0)return;
			System.out.println(countGoldbach(getPrime(n)));
		}
	}
	
	public static void main(String[] args) {
		new Main().io();
	}
	
	void debug(Object... os){
		System.out.println(Arrays.deepToString(os));
	}
}