#include <iostream>
using namespace std;
int a[100006];
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++) {
                a[x*x+y*y+z*z+x*y+y*z+z*x]++;
            }
        } 
    }
    for (int i=1; i<=N; i++) {
        cout << a[i] << endl;
    }
}
### Prompt

Your challenge is to write 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 a[100006];
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++) {
                a[x*x+y*y+z*z+x*y+y*z+z*x]++;
            }
        } 
    }
    for (int i=1; i<=N; i++) {
        cout << a[i] << endl;
    }
}
```