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 num[1000000] = {false};
  for(int i=2; i<1000; i++) if(!num[i]) for(int j=i*i; j<1000001; j+=i) num[j] = true;
  num[0] = num[1] = true;
  int n;
  while(cin >>n,n){
    int ans = 0;
    for(int i=2; i<=n/2; i++) if(!num[i] && !num[n-i]) ans++;
    cout <<ans<<endl;
  }
  return 0;
}