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.*;

import java.lang.*;

import java.math.*;



public class Main {

	Scanner sc = new Scanner(System.in);

	void run(){

		boolean[] np=new boolean[50001];

		np[0]=np[1]=true;

		for(int i = 0; i < 50001;i++){

			if(np[i]) continue;

			for(int j=i*2;j<50001;j+=i){

				np[j] = true;

			}

		}

		int[] dp = new int[50001];

		for(int i=0;i<50001;i++){

			if(np[i]) continue;

			for(int j=i;i+j<50001;j++){

				if(np[j])continue;

				dp[i+j]++;

			}

		}

		for(;;){

			int n = sc.nextInt();

			if(n==0) break;

			System.out.println(dp[n]);

		}

	}

	public static void main(String[] args){

		Main m = new Main();

		m.run();

	}

}