#include <vector>
#include <iostream>
using namespace std;
 
int ans[10005];
 
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 a = x*x + y*y + z*z + x*y + x*z + y*z;
    if (a <= 10000) ans[a]++;
  }
  
  for (int i = 1; i <= N; i++) cout << ans[i] << endl;
  return 0;
}
### 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 <vector>
#include <iostream>
using namespace std;
 
int ans[10005];
 
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 a = x*x + y*y + z*z + x*y + x*z + y*z;
    if (a <= 10000) ans[a]++;
  }
  
  for (int i = 1; i <= N; i++) cout << ans[i] << endl;
  return 0;
}
```