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
// 2011/04/04 Tazoe

#include <iostream>
using namespace std;

void eratos(bool prime[], int n)
{
	if(n>=1)
		prime[0] = false;
	if(n>=2)
		prime[1] = false;

	for(int i=2; i<n; i++)
		prime[i] = true;

	for(int i=2; i<n; i++){
		if(!prime[i])
			continue;
		for(int j=i+i; j<n; j+=i)
			prime[j] = false;
		if(n<i*i)
			return;
	}
}

int main()
{
	bool prime[50001];
	eratos(prime, 50001);

	while(true){
		int n;
		cin >> n;
		if(n==0)
			break;

		int cnt = 0;
		for(int i=2; i<=n-i; i++)
			if(prime[i]&&prime[n-i])
				cnt++;

		cout << cnt << endl;
	}

	return 0;
}