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
#include <iostream>

using namespace std;

bool isprime(int n) {
	for (int i = 2; i * i <= n; i++)
		if (n % i == 0)
			return false;
	return n != 1;
}

int main() {
	int n;
	bool prime[50000];
	for (int i = 2; i < 50000; i++)
		if (isprime(i))
			prime[i] = true;
		else
			prime[i] = false;
	while (cin >> n && n) {
		int ans = 0;
		for (int i = 2; i * 2 <= n; i++)
			if (prime[i] && prime[n-i])
				ans++;
		cout << ans << endl;
	}


	return 0;
}