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 is_prime[100000];
   is_prime[0]=is_prime[1]=false;
   for(int i=2;i<100000;i++)
      is_prime[i]=true;
   for(int i=2;i*i<100000;i++){
      if(is_prime[i]){
         for(int j=i*i;j<100000;j+=i){
            is_prime[j]=false;
         }
      }
   }
   while(true){
      int count=0;
      int n;
      cin >> n;
      if(n==0){
         break;
      }else{
         for(int i=2;i<n/2+1;i++){
            if(is_prime[i]&&is_prime[n-i])
                count++;
          }
         cout << count << endl;
      }
   }
   return 0;
}