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 <string.h>

using namespace std;
bool IsPrime[50001];

void calc()
{
	memset(IsPrime, 1, sizeof(IsPrime));
	IsPrime[0] = false;
	IsPrime[1] = false;
	for(int i = 2; i < 50001; ++i)
	{
		if(IsPrime[i])
		{
			for(int j = 2 * i; j < 50001; j += i)
			{
				IsPrime[j] = false;
			}
		}
	}
}

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

int main()
{
	solve();
	return(0);
}