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

int N, ans[10004];

int main() {
	cin >> N;

	for (int x=1; x<=100; x++) for (int y=1; y<=100; y++) for (int z=1; z<=100; z++) {
		ans[min(10001, x*x + y*y + z*z + x*y + y*z + z*x)]++;
	}

	for (int i=1; i<=N; i++) cout << ans[i] << '\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 N, ans[10004];

int main() {
	cin >> N;

	for (int x=1; x<=100; x++) for (int y=1; y<=100; y++) for (int z=1; z<=100; z++) {
		ans[min(10001, x*x + y*y + z*z + x*y + y*z + z*x)]++;
	}

	for (int i=1; i<=N; i++) cout << ans[i] << '\n';
}

```