#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
int n,a[2000005],ans;
int main()
{  cin>>n;
   for(int i=1;i<=100;i++)
   {  for(int j=1;j<=100;j++)
       {  for(int k=1;k<=100;k++)
           {  int x=i*i+j*j+k*k+i*j+i*k+j*k;
               a[x]++;
           }

       }
   }
   for(int i=1;i<=n;i++)
   {  cout<<a[i]<<endl;

   }
}
### Prompt

Generate a CPP solution to the following problem:

Let f(n) be the number of triples of integers (x,y,z) that satisfy both of the following conditions:

* 1 \leq x,y,z
* x^2 + y^2 + z^2 + xy + yz + zx = n



Given an integer N, find each of f(1),f(2),f(3),\ldots,f(N).

Constraints

* All values in input are integers.
* 1 \leq N \leq 10^4

Input

Input is given from Standard Input in the following format:


N


Output

Print N lines. The i-th line should contain the value f(i).

Example

Input

20


Output

0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
3
3
0
0

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
int n,a[2000005],ans;
int main()
{  cin>>n;
   for(int i=1;i<=100;i++)
   {  for(int j=1;j<=100;j++)
       {  for(int k=1;k<=100;k++)
           {  int x=i*i+j*j+k*k+i*j+i*k+j*k;
               a[x]++;
           }

       }
   }
   for(int i=1;i<=n;i++)
   {  cout<<a[i]<<endl;

   }
}
```