#include <bits/stdc++.h>

using namespace std;

int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);

	int n;
	cin >> n;
	map<int, int> mp;
	for(int i =1; i<=100; ++i) {
		for(int j =1; j<=100; ++j) {
			for(int k =1; k<=100; ++k) {
				mp[i * i + j * j + k * k + i * j + i * k + j * k]++;
			}
		}
	}
	for(int i =1; i<=n; ++i) cout << mp[i] << '\n';
}
### Prompt

Generate 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() {
	ios::sync_with_stdio(false);
	cin.tie(0);

	int n;
	cin >> n;
	map<int, int> mp;
	for(int i =1; i<=100; ++i) {
		for(int j =1; j<=100; ++j) {
			for(int k =1; k<=100; ++k) {
				mp[i * i + j * j + k * k + i * j + i * k + j * k]++;
			}
		}
	}
	for(int i =1; i<=n; ++i) cout << mp[i] << '\n';
}
```