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 main()
{
	int Pnum[50001] = {1,1,0}, n, ans;

	for (int i = 2; i < 50001; i++) {
		if (!(Pnum[i])) {
			for (int j = i+i; j < 50001; j+=i) {
				Pnum[j] = 1;
			}
		}
	}

	while (1) {
		cin >> n;
		if (n == 0)	break;

		ans = 0;
		for (int i = 2; i < n; i++) {
			if (!(Pnum[i]) && !(Pnum[n - i])){
				ans++;

				if (i == n - i) {
					ans++;
				}
			}
		}

		cout << ans/2 << endl;
	}

	return 0;
}