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<vector>

using namespace std;

int main()
{
	int n;
	vector<int> prime;
	int i,j;
	
	for(i=0;i<1000000;i++)
	{
		prime.push_back(1);
	}
	prime[0]=prime[1]=0;
	
	for(i=0;i<1000000;i++)
	{
		if(prime[i]==1)
		{
			for(j=2;j*i<1000000;j++)
			{
				prime[i*j]=0;
			}
		}
	}
	
	for(;;)
	{
		cin >> n ;
		if(n==0)
			break;
		
		int ans=0;
		
		for(i=0;i<=n-i;i++)
		{
			if(prime[i]==1)
			{
				if(prime[n-i]==1)
				{
					ans++;
//					cout << "f1:" << i << " f2:" << n-i << " ans:" << ans << endl;
				}
			}
		}
		
		cout << ans << endl;
		
	}
}