#include<bits/stdc++.h>

using namespace std;

int main()
{
	int n;
	cin>>n;

	map<int, int> hash;

	for(int x=1; x<=100; x++)
	{
		for(int y=1; y<=100; y++)
		{
			for(int z=1; z<=100; z++)
			{
				int ans = x*x + y*y + z*z + x*y + y*z + z*x;
				hash[ans]++;
			}
		}
	}

	for(int i=1; i<=n; i++)
	{
		printf("%d\n", hash[i]);
	}
	return 0;
}
### Prompt

Create a solution in cpp for 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()
{
	int n;
	cin>>n;

	map<int, int> hash;

	for(int x=1; x<=100; x++)
	{
		for(int y=1; y<=100; y++)
		{
			for(int z=1; z<=100; z++)
			{
				int ans = x*x + y*y + z*z + x*y + y*z + z*x;
				hash[ans]++;
			}
		}
	}

	for(int i=1; i<=n; i++)
	{
		printf("%d\n", hash[i]);
	}
	return 0;
}
```