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 x[100000], y[100000], n, sum;
int main() {
	for (int i = 2; i < 100000; i++) {
		for (int j = 2; j <= sqrt(i); j++) {
			if (i%j == 0) {
				goto E;
			}
		}
		x[i] = 1;
	E:;
	}
	while (true) {
		cin >> n; sum = 0; if (!n) { break; }
		for (int i = 2; i <= n / 2; i++) {
			if (x[i] == 1 && x[n - i] == 1) {
				sum++;
			}
		}
		cout << sum << endl;
	}
}