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;
#define MAX 50100

bool isPrime(int n){
    for(int i = 2; i * i <= n; i++){
        if(n % i == 0) return false;
    }
    return true;
}

int main(void){
    int d[MAX] = {0};
    for(int i = 2; i < MAX; i++) d[i] = isPrime(i);

    while(true){
        int n;
        cin >> n;
        if(n == 0) break;
        
        int c = 0;
        for(int i = 1; i <= n / 2; i++){
            if(d[i] == 1 && d[n - i] == 1) c++;
        }
        cout << c << endl;
    }
}
