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() {
	bool is_prime[1000000];

	is_prime[0] = is_prime[1] = false;
	for (int i = 2; i < 1000000; i++) {
		is_prime[i] = true;
	}

	for (int i = 2; i*i < 1000000; i++) {
		if (is_prime[i]) {
			for (int j = i*i; j < 1000000; j += i) {
				is_prime[j] = false;
			}
		}
	}

	int n_prime[1000000];

	while (true) {
		int n;
		cin >> n;

		if (cin.eof())
			break;
		if(n==0)
			break;

		int c=0;

		for(int i=0;i<=n/2;i++){
			if(is_prime[i]&&is_prime[n-i])
				c++;
		}

		cout << c << endl;
		
	}
	return 0;

}