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 static java.util.Arrays.*;
import static java.lang.Math.*;

public class Main{
 boolean[] p;
 int MAX = 50001;
 void run() {
  p = new boolean[MAX];
  for(int i=2;i<MAX;i++) if(!p[i]) {
   for(int j=2*i;j<MAX;j+=i) p[j] = true;
  }
  Scanner sc = new Scanner(System.in);
  for(;;) {
   int n = sc.nextInt();
   if( n == 0 ) break;

   int cnt = 0;
   for(int i=2;i<(n+1)/2;i++) if(!p[n-i] && !p[i]) cnt++;
   if(n/2 == n-n/2 && !p[n/2]) cnt++;
   System.out.println(cnt);
  }
 }
 public static void main(String[] args) {
  new Main().run();
 }
}