#include<iostream>
#include<math.h>
using namespace std;



int main(){
  bool is_prime[50001];
  is_prime[0]=false;is_prime[1]=false;
  for(int i=2;i<50001;i++)is_prime[i]=true;
  for(int i=2;i<=sqrt(50001);i++){
    if(is_prime[i]){
      for(int j=2;i*j<=50001;j++)is_prime[i*j]=false;
    }
  }


  int n;
  while(1){
    cin>>n;
    if(n==0)break;
    int cnt=0;

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


### Prompt

Please create a solution in CPP to the following problem:

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

### Response

```cpp
#include<iostream>
#include<math.h>
using namespace std;



int main(){
  bool is_prime[50001];
  is_prime[0]=false;is_prime[1]=false;
  for(int i=2;i<50001;i++)is_prime[i]=true;
  for(int i=2;i<=sqrt(50001);i++){
    if(is_prime[i]){
      for(int j=2;i*j<=50001;j++)is_prime[i*j]=false;
    }
  }


  int n;
  while(1){
    cin>>n;
    if(n==0)break;
    int cnt=0;

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


```