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.Scanner;

class Main {
    private static boolean[] calcPrimeTable(int n) {
        boolean[] table = new boolean[n + 1];
        for (int i = 2; i <= Math.sqrt(n); i++) {
            if (!table[i]) {
                for (int j = i + i; j <= n; j += i) {
                    table[j] = true;
                }
            }
        }
        return table;
    }

    private static void solve() {
        boolean[] table = calcPrimeTable(50000);
        Scanner scanner = new Scanner(System.in);
        while (true) {
            int n = scanner.nextInt();
            int counter = 0;
            if (n == 0) {
                break;
            }
            for (int i = 2; i <= n / 2; i++) {
                if (!table[i] && !table[n - i]) {
                    counter++;
                }
            }
            System.out.println(counter);
        }
    }

    public static void main(String... args) {
        solve();
    }
}