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 i,j,n,a[50000];
  a[0] = 0;
  a[1] = 0;
  for(i=2;i<50000;i++) a[i] = 1;
  for(i=2;i<=25000;i++){
    if(a[i] == 1){
      for(j=i*2;j<50000;j+=i) a[j] = 0;
    }
  }

  while(1){
    int ans;
    cin >> n;
    if(n == 0) break;
    ans = 0;
    for(i=2;i*2<=n;i++){
      if(a[i] == 1 && a[n-i] == 1) ans++;
    }
    cout << ans << endl;
  }

  return 0;
}