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 {

    static boolean [] primes;

    static void makePrimeList() {

        for(int i = 0; i < 50001; i++) {
            primes[i] = true;
        }

        primes[0] = false;
        primes[1] = false;

        for(int n = 2; n < 50001; n++) {
            if (primes[n]) {
                for(int k = 2 * n; k < 50001; k += n) {
                    primes[k] = false;
                }
            }
        }

    }

    static void solve (int n) {

        int result = 0;

        for(int i = 2; i <= n / 2; i++) {
            if (primes[i] && primes[n-i]) result += 1;
        }

        System.out.println(result);
    }

    public static void main (String [] args) {

        Scanner sc = new Scanner(System.in);

        primes = new boolean[50001];
        makePrimeList();

        while (true) {
            int n = sc.nextInt();

            if ( n == 0 )   break;

            solve(n);
        }

    }
}