#include <bits/stdc++.h>

using namespace std;

int ans[10001];

int main() {
	for(int a = 1; a <= 100; a++) {
		for(int b = 1; b <= 100; b++) {
			for(int c = 1; c <= 100; c++) {
				int x = a*a + b*b + c*c + a*b + b*c + c*a;
				if(x <= 10000) ans[x]++;
			}
		}
	}
	int n;
	cin >> n;
	for(int i = 0; i < n; i++) cout << ans[i+1] << '\n';
}
### Prompt

Please create a solution in cpp 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 ans[10001];

int main() {
	for(int a = 1; a <= 100; a++) {
		for(int b = 1; b <= 100; b++) {
			for(int c = 1; c <= 100; c++) {
				int x = a*a + b*b + c*c + a*b + b*c + c*a;
				if(x <= 10000) ans[x]++;
			}
		}
	}
	int n;
	cin >> n;
	for(int i = 0; i < n; i++) cout << ans[i+1] << '\n';
}
```