#include <bits/stdc++.h>
using namespace std;

int a[111111];
int main() {
    int n;
    cin >> n;
    for(int x = 1; x < 101; x++)
        for(int y = 1; y < 101; y++)
            for(int z = 1; z < 101; z++)
                a[x * (x + y + z) + y * (y + z) + z * z]++;
    for(int i = 0; i < n; i++)
        cout << a[i + 1] << '\n';
    return 0;
}

### Prompt

Your task is to create 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 <bits/stdc++.h>
using namespace std;

int a[111111];
int main() {
    int n;
    cin >> n;
    for(int x = 1; x < 101; x++)
        for(int y = 1; y < 101; y++)
            for(int z = 1; z < 101; z++)
                a[x * (x + y + z) + y * (y + z) + z * z]++;
    for(int i = 0; i < n; i++)
        cout << a[i + 1] << '\n';
    return 0;
}

```