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;

#define Max 50000
bool IsPrime[Max];

int main()
{
	for (int i = 2; i < Max; i++) IsPrime[i] = true;
	for (int i = 2; i < Max; i++)
	{
		if (!IsPrime[i]) continue;
		for (int j = i + i; j < Max; j += i)
		{
			IsPrime[j] = false;
		}
	}

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

	return 0;
}