#include <bits/stdc++.h>
using namespace std;
int main(void){
    // Your code here!
 int i,j,k,n;
 map<int,int> m;
 for(i=1;i<=100;i++)
 {
  for(j=1;j<=100;j++)
  {
   for(k=1;k<=100;k++)
   m[(i*i)+(j*j)+(k*k)+(i*j)+(j*k)+(k*i)]++;
  }
 }
 cin >> n;
 for(i=1;i<=n;i++)
 cout << m[i] << '\n';
 return 0;
}
### 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(void){
    // Your code here!
 int i,j,k,n;
 map<int,int> m;
 for(i=1;i<=100;i++)
 {
  for(j=1;j<=100;j++)
  {
   for(k=1;k<=100;k++)
   m[(i*i)+(j*j)+(k*k)+(i*j)+(j*k)+(k*i)]++;
  }
 }
 cin >> n;
 for(i=1;i<=n;i++)
 cout << m[i] << '\n';
 return 0;
}
```