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
// 2020/05/18 Tazoe

#include <iostream>
using namespace std;

int main()
{
	bool is_prime[50001];

	is_prime[0] = is_prime[1] = false;
	for(int i=2; i<50001; i++){
		is_prime[i] = true;
	}

	for(int i=2; i*i<50001; i++){
		if(is_prime[i]){
			for(int j=i*i; j<50001; j+=i){
				is_prime[j] = false;
			}
		}
	}

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

		if(n==0)
			break;

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

		cout << cnt << endl;
	}

	return 0;
}

