#include <iostream>
using namespace std;

int cnt[1145140];

int main() {
	int n;
	cin >> n;
	
	for (int x = 1; x <= 100; x++) {
		for (int y = 1; y <= 100; y++) {
			for (int z = 1; z <= 100; z++) {
				int res = x * x + y * y + z * z + x * y + y * z + z * x;
				cnt[res]++;
			}
		}
	}
	
	for (int i = 1; i <= n; i++) cout << cnt[i] << endl;
	return 0;
}
### Prompt

In CPP, your task is to solve 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 <iostream>
using namespace std;

int cnt[1145140];

int main() {
	int n;
	cin >> n;
	
	for (int x = 1; x <= 100; x++) {
		for (int y = 1; y <= 100; y++) {
			for (int z = 1; z <= 100; z++) {
				int res = x * x + y * y + z * z + x * y + y * z + z * x;
				cnt[res]++;
			}
		}
	}
	
	for (int i = 1; i <= n; i++) cout << cnt[i] << endl;
	return 0;
}
```