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;

const int max_lim = 50001;
bool prime[max_lim];

void init()
{
    for (int i = 0; i < max_lim; i++)
        prime[i] = true;
    prime[0] = prime[1] = false;

    for (int i = 2; i * i < max_lim; i++) 
        for (int j = 2 * i; j < max_lim; j += i)
            prime[j] = false;
}

int main()
{
    int n;

    init();
    while (cin >> n, n) {
        int ans = 0;
        for (int i = 2; 2 * i <= n; i++) 
            if (prime[i] && prime[n - i] && n - i > 0) 
                ans++;
        cout << ans << endl;
    }

    return 0;
}