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;

const int MAX = 50000;

void eratosthenes(bool* p)
{
	for (int i=0; i<=MAX; i++) p[i] = true;
	p[1] = false;
	for (int i=2; i<=MAX; i++) {
		if (!p[i]) continue;
		for (int d=2; i*d<=MAX; d++) p[i*d] = false;
	}
}

int main()
{
	int n;
	
	bool *is_prime = new bool[MAX+1];
	if (is_prime == NULL) return 1;
	eratosthenes(is_prime);
	
	while (true) {
		cin >> n;
		if (n==0) break;
		
		int count = 0;
		for (int i=2; i<=n/2; i++) {
			if (is_prime[i] && is_prime[n-i]) count++;
		}
		
		cout << count << endl;
	}
	
	delete[] is_prime;
	
	return 0;
}