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<bits/stdc++.h>
#define rep(i,n)for(int i=0;i<n;i++)
using namespace std;
typedef pair<int, int>P;

bool is_prime[50001];
int main() {
	memset(is_prime, 1, sizeof(is_prime));
	is_prime[0] = is_prime[1] = false;
	for (int i = 2; i <= 50000; i++) {
		if (is_prime[i]) {
			for (int j = i * 2; j <= 50000; j += i)is_prime[j] = false;
		}
	}
	int n;
	while (cin >> n, n) {
		int cnt = 0;
		for (int i = 2; i <= n / 2; i++) {
			if (is_prime[i] && is_prime[n - i])cnt++;
		}
		cout << cnt << endl;
	}
	return 0;
}