#include <iostream>
using namespace std;
int main() {
  int N, v[10001]{};
  cin >> N;
  for (int x = 1; x != 100; ++x) {
    for (int y = 1; y != 100; ++y) {
      for (int z = 1; z != 100; ++z) {
        int f = x * x + y * y + z * z + x * y + y * z + z * x;
        if (f <= N) ++v[f];
      }
    }
  }
  for (int n = 1; n <= N; ++n) cout << v[n] << endl;
}

### 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 <iostream>
using namespace std;
int main() {
  int N, v[10001]{};
  cin >> N;
  for (int x = 1; x != 100; ++x) {
    for (int y = 1; y != 100; ++y) {
      for (int z = 1; z != 100; ++z) {
        int f = x * x + y * y + z * z + x * y + y * z + z * x;
        if (f <= N) ++v[f];
      }
    }
  }
  for (int n = 1; n <= N; ++n) cout << v[n] << endl;
}

```