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[50000];

  is_prime[0] = is_prime[1] = false;
  for(int i=2; i<50000; i++){
    is_prime[i] = true;
  }

  for(int i=2; i*i<50000; i++){
    if(is_prime[i]){
      for(int j=i*i; j<50000; j+=i){
	is_prime[j] = false;
      }
    }
  }

  while(true){
    int n;
    cin >> n;

    if(n==0)
      break;

    int cnt = 0;
    for(int i=2; i<=n/2; i++){
      if(is_prime[i] && is_prime[n-i]){
	cnt++;
      }
    }

    cout << cnt <<endl;
  }

  return 0;
}

    

