#include <bits/stdc++.h>
using namespace std;

int main() {
  vector<int> a(10000);
  int N, b, c = 0;
  cin >> N;
  for (int x = 1; x < 99; x++) for (int y = 1; y < 99; y++) for (int z = 1; z < 99; z++) {
    b = x * x + y * y + z * z + x * y + y * z + z * x - 1;
    if (b < 10000) a.at(b)++;
  }
  for (; c < N; c++) cout << a.at(c) << endl; 
}
### Prompt

Your challenge is to write 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 main() {
  vector<int> a(10000);
  int N, b, c = 0;
  cin >> N;
  for (int x = 1; x < 99; x++) for (int y = 1; y < 99; y++) for (int z = 1; z < 99; z++) {
    b = x * x + y * y + z * z + x * y + y * z + z * x - 1;
    if (b < 10000) a.at(b)++;
  }
  for (; c < N; c++) cout << a.at(c) << endl; 
}
```