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>

using namespace std;

int main() {

    bool P[50001];
    fill(P, P + 50001, true);
    P[0] = P[1] = false;

    for (int i = 2; i * i <= 50000; i++) {
        if (P[i]) {
            for (int j = i * 2; j <= 50000; j += i) {
                P[j] = false;
            }
        }
    }

    int n;
    while (cin >> n) {
        if (n == 0) break;
        int ans = 0;
        for (int i = 2; i <= n / 2; i++) {
            if (P[i] && P[n - i]) ans++;
        }
        cout << ans << endl;
    }
}

