#include <iostream>

using namespace std;
int t, n;
int d[10001];

int main()
{
   cin >> n;
   for (int x = 1; x*x <= n; x++)
   for (int y = 1; y*y <= n; y++)
   for (int z = 1; z*z <= n; z++)
    {
        t = x*x+y*y+z*z+x*y+y*z+z*x;
        if (t > n) break;
        d[t]++;
    }
   for (int i = 1 ; i <= n; i++)
    cout << d[i] << endl;
   
   return 0;
}
### 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 <iostream>

using namespace std;
int t, n;
int d[10001];

int main()
{
   cin >> n;
   for (int x = 1; x*x <= n; x++)
   for (int y = 1; y*y <= n; y++)
   for (int z = 1; z*z <= n; z++)
    {
        t = x*x+y*y+z*z+x*y+y*z+z*x;
        if (t > n) break;
        d[t]++;
    }
   for (int i = 1 ; i <= n; i++)
    cout << d[i] << endl;
   
   return 0;
}
```