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 a[50001];

int main(void)
{
	a[0]=a[1]=1;
	for(int i=2;i<=50000;i++)
	{
		for(int j=i+i;j<=50000;j+=i)
		{
			a[j]=1;
		}
	}
	while(1)
	{
		int n;
		cin>>n;
		if(n==0)break;
		int ans=0;
		for(int i=2;i<=n/2;i++)
		{
			if(a[i]==0&&a[n-i]==0)
				ans++;
		}
		cout<<ans<<endl;
	}
}