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 a[100000];

  a[0]=a[1]=false;
  for(int i=2;i<100000;i++){
    a[i]=true;
  }

  for(int i=2;i*i<100000;i++){
    if(a[i]){
      for(int j=i*i;j<100000;j+=i){
        a[j]=false;
      }
    }
  }

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

    if(m==0){
      break;
    }

    for(int i=2;i<=m/2;i++){
      if(a[i]){
        if(a[m-i]){
          count++;
        }
      }
    }

    cout<<count<<endl;

  }

  return 0;
}

