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 primes[50000]={false};
    primes[0] = true;
    for(int i=2;i <= 25000;++i) {
        if (primes[i-1]) continue;
        for(int j=i+i;j <= 50000;j+=i) {
            primes[j-1] = true;
        }
    }

    int n;
    while (cin >> n && n) {
        int cnt = 0;
        for(int i=2; i <= n/2;++i) {
            if (!primes[i-1] && !primes[n-i-1]) {
                ++cnt;
            }
        }
        cout << cnt << endl;
    }

    return 0;
}