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.*;

class Main{
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    while (true) {
      int n = sc.nextInt();
      if (n == 0) {
        break;
      }
      boolean[] isPrime = new boolean[n+1];
      for (int i = 2; i <= n; i++) {
        isPrime[i] = true;
      }
      for (int i = 2; i*i <= n; i++) {
        if(isPrime[i]) {
          for (int j = 2*i; j <= n; j += i) {
            isPrime[j] = false;
          }
        }
      }
      int counter = 0;
      for (int i = 1; i <= n/2; i++) {
        if(isPrime[i] && isPrime[n-i]) {
          counter++;
        }
      }
      System.out.println(counter);
    }
  }
}