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

int n, c[10001];

int main() {
	cin >> n;
	for (int x = 1; x < 101; ++x)
		for (int y = 1; y < 101; ++y)
			for (int z = 1; z < 101; ++z) {
				int t = x * x + y * y + z * z + x * y + y * z + z * x;

				if (t <= n)
					++c[t];
			}
	for (int i = 1; i <= n; ++i)
		cout << c[i] << endl;
}

### Prompt

Construct a cpp code solution to the problem outlined:

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;
using ll = long long;

int n, c[10001];

int main() {
	cin >> n;
	for (int x = 1; x < 101; ++x)
		for (int y = 1; y < 101; ++y)
			for (int z = 1; z < 101; ++z) {
				int t = x * x + y * y + z * z + x * y + y * z + z * x;

				if (t <= n)
					++c[t];
			}
	for (int i = 1; i <= n; ++i)
		cout << c[i] << endl;
}

```