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

int main() {
  int N; cin >> N;
  int ans[100000];
  
  for(int i = 1; i*i< N; i++){
    for(int j = 1; j*j < N;j++){
      for(int k = 1; k*k < N;k++){
        int total = i*i+j*j+k*k+j*k+j*i+i*k;
        ans[total]++;
      }
    }    
  }
  for(int i = 1; i <= N; i++){
    cout << ans[i] << endl;
  }
}

### Prompt

Construct a CPP code solution to the problem outlined:

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 ans[100000];
  
  for(int i = 1; i*i< N; i++){
    for(int j = 1; j*j < N;j++){
      for(int k = 1; k*k < N;k++){
        int total = i*i+j*j+k*k+j*k+j*i+i*k;
        ans[total]++;
      }
    }    
  }
  for(int i = 1; i <= N; i++){
    cout << ans[i] << endl;
  }
}

```