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>
#include <vector>
using namespace std;

int main()
{
	vector<bool> is_not_prime(50001);
	is_not_prime[1] = true;
	for (int i = 2; i <= 50000; ++i)
	{
		if (!is_not_prime[i])
		{
			for (int j = 2 * i; j <= 50000; j += i)
			{
				is_not_prime[j] = true;
			}
		}
	}

	while (true)
	{
		int n;
		cin >> n;
		if (n == 0)
		{
			return 0;
		}
		int count = 0;
		for (int i = 2; i <= n / 2; ++i)
		{
			if (!is_not_prime[i] && !is_not_prime[n - i])
				++count;
		}
		cout << count << endl;
	}
}