#include<cstdio>
#include<cmath>
#include<vector>
using namespace std;
const int upto=50000;
int main(){
    vector<bool> prs(upto+1,true);
    prs[0]=prs[1]=false;
    for(int i=2;i<=sqrt(upto);i++){
        if(prs[i]){
            for(int j=i*i;j<=upto;j+=i)prs[j]=false;
        }
    }
    for(;;){
        int n;
        scanf("%d",&n);
        if(n==0)break;
        int ans=0;
        for(int i=2;i<=n/2;i++){
            if(prs[i]&&prs[n-i])ans++;
        }
        printf("%d\n",ans);
    }
}
### 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<cstdio>
#include<cmath>
#include<vector>
using namespace std;
const int upto=50000;
int main(){
    vector<bool> prs(upto+1,true);
    prs[0]=prs[1]=false;
    for(int i=2;i<=sqrt(upto);i++){
        if(prs[i]){
            for(int j=i*i;j<=upto;j+=i)prs[j]=false;
        }
    }
    for(;;){
        int n;
        scanf("%d",&n);
        if(n==0)break;
        int ans=0;
        for(int i=2;i<=n/2;i++){
            if(prs[i]&&prs[n-i])ans++;
        }
        printf("%d\n",ans);
    }
}
```