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>
#include<cstdio>
#include<algorithm>
using namespace std;
bool prime[50001];
void eratosutenesu(){
	fill(prime, prime + 50001, true);
	prime[0] = false; prime[1] = false;
	for(int i = 2; i * i <= 50000; i++){
		if(prime[i] == true){
			for(int j = 2;; j++){
				if(j * i > 50000) break;
				prime[j * i] = false;
			}
		}
	}
	return;
}
int main(){
	eratosutenesu();
	for(;;){
		int n;
		cin >> n;
		if(n == 0) break;
		int ans = 0;
		for(int i = 1; i <= n / 2; i++){
			if(prime[i] && prime[n - i]) ans++;
		}
		cout << ans << endl;
	}
	return 0;
}