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<cmath>
#include<vector>
int main()
{
	std::vector<bool>is_prime(50020, true);
	const int root = static_cast<int>(floor(sqrt(50021)));
	for (int i = 0; i <= root - 2; i++)
	{
		if (is_prime[i])
		{
			for (int j = i + 2; (i + 2) * j < 50021; j++)
			{
				is_prime[(i + 2) * j - 2] = false;
			}
		}
	}
	while (true)
	{
		int n;
		std::cin >> n;
		if (n == 0)
		{
			break;
		}
		int cnt = 0;
		for (int i = 0; i < n; i++)
		{
			if (is_prime[i] && is_prime[n - i - 4])cnt++;
			if (i + 2 >= n / 2)break;
		}
		std::cout << cnt << std::endl;
	}
	return 0;
}
