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>
using namespace std;

using db = double;
using ll = long long;
using vi = vector <int>;
#define op operator
#define pb push_back

const int N = 5e4L + 11;
int p[N];

int main() {
	iota(p, p + N, 0);
	for(int i = 2; i < N; i ++) if(p[i] == i)
		for(int j = i; j < N; j += i) p[j] = i;

	cout << fixed << setprecision(9);
	ios :: sync_with_stdio(0);

	for(int n; cin >> n && n; ) {
		int ans = 0;
		for(int i = 2; i * 2 <= n; i ++)
			if(p[i] == i && p[n - i] == n - i)
				ans ++;
		cout << ans << '\n';
	}

	return 0;
}