#include <bits/stdc++.h>
using namespace std;
int n, a[3000005];

int main(){
	cin >> n;
	for(int i = 1; i <= 142; i++)
		for(int j = 1; j <= 142; j++)
			for(int k = 1; k <= 142; k++)
				a[i * i + j * j + k * k + i * j + j * k + k * i]++;
	for(int i = 1; i <= n; i++)
		printf("%d\n", a[i]);
	return 0;
}
### 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;
int n, a[3000005];

int main(){
	cin >> n;
	for(int i = 1; i <= 142; i++)
		for(int j = 1; j <= 142; j++)
			for(int k = 1; k <= 142; k++)
				a[i * i + j * j + k * k + i * j + j * k + k * i]++;
	for(int i = 1; i <= n; i++)
		printf("%d\n", a[i]);
	return 0;
}
```