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.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;

class Main {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        boolean[] nonPrime = new boolean[50001];
        nonPrime[0] = true;
        nonPrime[1] = true;

        for (int i = 2; i <= 25000; i++) {
            if (nonPrime[i]) {
                continue;
            }

            for (int j = i + i; j <= 50000; j += i) {
                nonPrime[j] = true;
            }
        }

        String line;
        while (!(line = br.readLine()).equals("0")) {
            int x = Integer.parseInt(line);
            int result = 0;

            if (x % 2 == 0) {
                for (int j = 2; j <= x / 2; j++) {
                    if (!nonPrime[j] && !nonPrime[x - j])
                        result++;
                }
            } else {
                if (!nonPrime[x - 2])
                    result++;
            }

            System.out.println(result);
        }
    }
}
