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 k[50001] ={1};
	int g,h;

	k[1] = 1;
	for (int i = 2; i < 50001; i++) {
		if (k[i] == 0) {
			for (int j = 2; j < (50000/i+1); j++) {
				k[i*j] = 1;
			}
		}
	}

	while (cin >> g) {
		if (g == 0) {
			break;
		}
		int counter = 0;
		for (int i = 2; i < 50001; i++) {
			if (i > g/2) {
				break;
			} else {
				if (k[i] == 0 && k[g-i] == 0) {
					counter++;
				}
			}
		}
		cout << counter << endl;
	}

	return 0;
}