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 {

	static boolean[] isPrime = new boolean[50001];
	static int[] a = new int[10];
	static{
		Arrays.fill(isPrime, true);
		isPrime[0]=isPrime[1]=false;
		for(int i = 2; i*i<= isPrime.length;i++){
			if(isPrime[i]){
				for(int j = i+i; j < isPrime.length;j+=i){
					isPrime[j]=false;
				}
			}
		}
		int count=0;
		for(int i = 0; i < isPrime.length;i++){
			if(isPrime[i]){
				count++;
			}
		}
		a = new int[count];
		count=0;
		for(int i = 0; i < isPrime.length;i++){
			if(isPrime[i]){
				a[count++]=i;
			}
		}
	}
	public static void main(String[] args) {
		Scanner cin = new Scanner(System.in);
		while(true){
			int n = cin.nextInt();
			if(n==0){
				break;
			}
			else if(n==4){
				System.out.println(1);
				continue;
				
			}
			int count=0;
			int lim = Arrays.binarySearch(a, n/2+1);
			if(lim < 0){
				lim = lim*(-1) -1;
			}
			for(int i = 0; i < lim;i++){
				if(Arrays.binarySearch(a, n-a[i]) > 0){
					count++;
				}
				
			}
			System.out.println(count);
		}
	}

}