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>

bool sieve[100000];
void makesieve();

int main()
{
	makesieve();
	while(1)
	{
		int n,ans=0;
		std::cin>>n;
		if(n==0)break;
		for(int i=0;i<=n/2;i++)
		{
			if(sieve[i]&&sieve[n-i])ans++;
		}
		std::cout<<ans<<std::endl;
	}
	return 0;
}

void makesieve()
{
	for(int i=0;i<100000;i++){sieve[i]=true;}
	sieve[0]=false;sieve[1]=false;
	for(int i=2;i<100000;i++)
	{
		for(int j=i*2;j<100000;j+=i)
		{
			sieve[j]=false;
		}
	}
}