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 <cmath>
using namespace std;

int main(){
	int n, prime[10000], flag[50005] = {}, cnt = 1;
	prime[0] = 2;
	flag[2] = 1;
	for (int i = 3; i < 50000; i += 2){
		int k = 0;
		for (int j = 3; j <= sqrt(i); j++) {
			if (i % j == 0){
				k = 1;
				break;
			}
		}
		if (!k) {
			flag[i] = 1;
			prime[cnt] = i;
			cnt++;
		}
	}
	while (1){
		cnt = 0;
		cin >> n;
		if (!n) break;
		for (int i = 0; prime[i] <= n / 2; i++){
			if (flag[n - prime[i]]) cnt++;
		}
		cout << cnt << endl;
	}
}