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;

/** Problem0056 : Goldbach's Conjecture **/
#define MAX 50000
int main()
{
	bool prime[MAX];
	int  input, count;
	
	for (int i=0; i<MAX; i++)
		prime[i] = true;
	
	prime[0] = false; prime[1] = false;
		
	for (int i=2; i<MAX; i++) {
		if (prime[i]) {
			for (int j=2; i*j<MAX; j++) {
				prime[i*j] = false;
			}
		}
	}
	
	while (1) {
		cin >> input;
		if (input == 0) break;
		
		count = 0;
		for (int i=2; i<=input/2; i++) {
			if (prime[i] && prime[input - i])
					count++;
		}
		
		cout << count << endl;
	}
	
	return 0;
}