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 <bits/stdc++.h>
using namespace std;

int main()
{
	vector<bool> prime(50001, true);
	prime[0] = prime[1] = false;
	for (int i = 2; i <= 223; i++) {
		if (prime[i]) {
			for (int j = i * 2; j <= 50000; j += i) {
				prime[j] = false;
			}
		}
	}
	int n, res;
	while (cin >> n, n) {
		res = 0;
		if (n % 2) {
			if (prime[n - 2])
				res = 2;
		}
		else if (n == 4) {
			res = 2;
		}
		else {
			for (int i = 3; i <= n - 3; i += 2) {
				if (prime[i] && prime[n - i]) {
					res++;
					if (i == n - i)
						res++;
				}
			}
		}
		cout << res / 2 << endl;
	}
	return 0;
}