#include <bits/stdc++.h>

using namespace std;

int main(){
    int n;
    cin >> n;
    int ar[n+1];
    memset(ar,0,sizeof(ar));
    for(int i=1;i<=100;i++) for(int j=1;j<=100;j++) for(int k=1;k<=100;k++){
        int res = i*i+j*j+k*k+i*j+i*k+j*k;
        if(res <= n) ar[res]++;
    }
    for(int i=1;i<=n;i++) cout << ar[i] << '\n';
}
### Prompt

Create a solution in CPP for 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 main(){
    int n;
    cin >> n;
    int ar[n+1];
    memset(ar,0,sizeof(ar));
    for(int i=1;i<=100;i++) for(int j=1;j<=100;j++) for(int k=1;k<=100;k++){
        int res = i*i+j*j+k*k+i*j+i*k+j*k;
        if(res <= n) ar[res]++;
    }
    for(int i=1;i<=n;i++) cout << ar[i] << '\n';
}
```