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()
{
	const int Max = 50010;
	bool prime[Max] = {false};
	
	for (int i = 2; i * i < Max; i++){
		for (int j = i * i; j < Max; j += i){
			prime[j] = true;
		}
	}
	
	int n;
	while (cin >> n, n){
		int count = 0;
		for (int i = 2; i <= n / 2; i++){
			if (!prime[i] && !prime[n - i]){
				count++;
			}
		}
		cout << count << endl;
	}
}