#include <bits/stdc++.h>
using namespace std;
int xyz[200000];
int main()
{
	int n;
	cin >> n;
	for (int i = 1; i <= 100; i++)
	{
		for (int j = 1; j <= 100; j++)
		{
			for (int k = 1; k <= 100; k++)
			{
				xyz[i * i + j * j + k * k + i * j + i * k + j * k]++;
			}
		}
	}
	for (int i = 1; i <= n; i++)
	{
		cout << xyz[i] << endl;
	}
	return 0;
}
### 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 xyz[200000];
int main()
{
	int n;
	cin >> n;
	for (int i = 1; i <= 100; i++)
	{
		for (int j = 1; j <= 100; j++)
		{
			for (int k = 1; k <= 100; k++)
			{
				xyz[i * i + j * j + k * k + i * j + i * k + j * k]++;
			}
		}
	}
	for (int i = 1; i <= n; i++)
	{
		cout << xyz[i] << endl;
	}
	return 0;
}
```