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 <numeric>
using namespace std;

#define SIZE 50001

int main() {
	bool prime[SIZE];
	fill(prime, prime + SIZE, true);
	prime[0] = prime[1] = false;
	for (int i = 2; i * i < SIZE; i++) {
		for (int j = 2; j * i < SIZE; j++) {
			if (!prime[i * j]) continue;
			prime[i * j] = false;
		}
	}

	int n, count;
	while (cin >> n) {
		if (n == 0) break;

		count = 0;
		for (int i = 0; i <= n / 2; i++) {
			if (prime[i] && prime[n - i]) count++;
		}
		cout << count << endl;
	}
	return 0;
}