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 MN 50001

int main()
{
	bool pr[MN] = {0};
	for(int i=2; i<MN; i++) pr[i]=1;

	for(int i=2; i*i<MN; i++)
	{
		if(pr[i])
		for(int j=i*2; j<MN; j+=i)
		{
			pr[j] = 0;
		}
	}

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