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(){
  int isPrime[50001];
  fill(isPrime,isPrime+50001,1);
  isPrime[0] = isPrime[1] = 0;
  for(int i = 2 ; i*i < 50001 ; i++ ){
    if(isPrime[i])for(int j = i*2 ; j < 50001 ; j+=i )isPrime[j] = 0;
  }
  int n;
  while(cin >> n,n){
    int cnt = 0;
    for(int i = 0 ; i <= n/2 ; i++ ){
      if(isPrime[i] == 1 && isPrime[n-i] == 1)cnt++; 
    }
    cout << cnt << endl;
  }
  return 0;
}