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[1000000]; //?´???°???????????¨

 is_prime[0] = is_prime[1] = false;
 
 for(int i=2; i<1000000; i++){
  is_prime[i] = true;
 }
 
 for(int i=2; i*i<1000000; i++){
  if(is_prime[i]){
   for(int j=i*i; j<1000000; j+=i){
    is_prime[j] = false;
   }
  }
 }

 while(true){
  int n;
  int count = 0;
  cin >> n;

  if(n==0) break;
  
  for(int i=2; i<=n/2; i++){
   if(is_prime[i]){
    if(is_prime[n-i]) count++;
   }
  }
  cout << count << endl;
 }
 

 return 0;
}