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;

int main() {
    int N = 50000;
    vector<int> primes;
    vector<bool> is_prime(N,true);

    for (int j=2; j<=N; j++) {
        if(is_prime[j]){
            for (int k=2; k<=N/j;k++){
                is_prime[j*k] = false;
            }
        }
    }

    while(1){
        int n;
        cin >> n;
        int m = n/2;
        if (n == 0) break;
        int res = 0;
        for (int j=2;j<=m;j++) {
            if(is_prime[j] && is_prime[n-j]){
                res++;
            }
        }
        cout << res << endl;
    }
}
