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 n;
	bool p[50001] = {false, false};
	
	for (int i = 2; i * i < 50001; i++){
		for (int j = i * i; j < 50001; j += i){
			p[j] = true;
		}
	}
	while (cin >> n, n){
		int c = 0;
		for (int i = 2; i <= n / 2; i++){
			if (!p[i] && !p[n - i]){
				c++;
			}
		}
		cout << c << endl;
	}
	return (0);
}