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<vector>
#include<string>
#define N 50001
using namespace std;

int main() {
	vector<bool>sosuu(N, true);
	for (int b = 2; b < N; b++) {
		if (sosuu[b]) {
			for (int c = b * 2; c < N; c += b)sosuu[c] = false;
		}
	}
	int d;
	while (cin >> d, d) {
		int s = 0;
		for (int e = 2; e <= d / 2; e++) {
			if (sosuu[e] && sosuu[d - e])s++;
		}
		cout << s << endl;
	}
}