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>

bool sosuu[50001];

void init(){
	for (int i = 0; i < 50001; i++)sosuu[i] = true;

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

int main(){

	init();

	int n;
	while (std::cin >> n, n){

		int cnt = 0;

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

		std::cout << cnt << std::endl;

	}

	return 0;
}