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 <cstdio>
#include <cstring>
using namespace std;
bool prime[50001];
void eratos(void)
{
	memset(prime,true,sizeof(prime));
	prime[0]=false;
	prime[1]=false;
	for(int i=2;i*i<50001;i++)
	{
		if(!prime[i])continue;
		for(int j=i*2;j<50001;j+=i)
		{
			prime[j]=false;
		}
	}
	return;
}
int main()
{
	eratos();
	int n,count;
	while(scanf("%d",&n)!=EOF)
	{
		if(n==0)break;
		count =0;
		for(int i=1;i<n/2+1;i++)
		{
			if(prime[i]&&prime[n-i])count++;
		}
		cout << count << endl;
	}
	return 0;
}