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>
#include <string>
#include <algorithm>

#define REP(i,k,n) for(int i=k;i<n;i++)
#define rep(i,n) for(int i=0;i<n;i++)
#define MAX 1000000
#define pb push_back

using namespace std;

int prime[MAX];

int main()
{
	prime[0] = prime[1] = 0;

	REP(i,2,MAX)
	{
		prime[i] = 1;
	}

	REP(i,2,MAX)
	{
		if(prime[i])
		{
			for(int j = i*2;j < MAX;j += i)
			{
				prime[j] = 0;
			}
		}
	}

	int n;
	while(cin >> n && n)
	{
		int count = 0;
		rep(i,(n/2)+1)
		{
			if(prime[i] == 1 && prime[n - i] == 1)
			{
				count++;
			}
		}
		cout << count << endl;
	}
	return 0;
}