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

int main() {
  int n;
  cin >> n;
  vector<int> a(n+1);
  
  for(int i=1;i<102;i++)
    for(int j=1;j<102;j++)
      for(int k=1;k<102;k++){
        int s;
        s = i*i + j*j + k*k + i*j + j*k + k*i;
        if(s<n+1)	a.at(s)+=1;
      }
  
  for(int i=1;i<n+1;i++)
    cout << a.at(i) << endl;
  
  return 0;
}

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

int main() {
  int n;
  cin >> n;
  vector<int> a(n+1);
  
  for(int i=1;i<102;i++)
    for(int j=1;j<102;j++)
      for(int k=1;k<102;k++){
        int s;
        s = i*i + j*j + k*k + i*j + j*k + k*i;
        if(s<n+1)	a.at(s)+=1;
      }
  
  for(int i=1;i<n+1;i++)
    cout << a.at(i) << endl;
  
  return 0;
}

```