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(){
    cin.tie(nullptr);
    ios::sync_with_stdio(false);

    int n;
    while(cin >> n){
        if(n == 0) return 0;
        vector<bool> F(n + 1, true);
        for(int i = 2; i <= (int)sqrt(n); i++){
            if(F[i]){
                for(int j = i + i; j <= n; j += i){
                    F[j] = false;
                }
            }
        }

        int ans = 0;
        for(int i = 2; i <= n / 2; i++){
            if(F[i] and F[n - i]) ans++;
        }

        cout << ans << endl;
    }

    return 0;
}
