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;

int main()
{
	int n;
	int p[50000] = {};

	for (int i = 2; i <= 50000; ++i)
	{
		if (p[i-2] == 0)
		{
			p[i-2] = 1;
			for (int j = i+i; j <= 50000; j += i) p[j-2] = -1;
		}
	}

	while (cin >> n && n)
	{
		int r = 0;
		for (int i = 2; i <= n/2; ++i) if (p[i-2] == 1 && p[n-i-2] == 1) ++r;
		cout << r << endl;
	}
	return 0;
}