#include <bits/stdc++.h>
using namespace std;
int ans[10001];
int main()
  {int N; 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)
    {auto n = x * x + y * y + z * z + x * y + y * z + z * x; if (n <= 10000) ++ans[n];}
  for (int n = 1; n <= N; ++n) cout << ans[n] << "\n";}
### Prompt

Your task is to create 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;
int ans[10001];
int main()
  {int N; 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)
    {auto n = x * x + y * y + z * z + x * y + y * z + z * x; if (n <= 10000) ++ans[n];}
  for (int n = 1; n <= N; ++n) cout << ans[n] << "\n";}
```