#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 1; i < (int)(n); i++)
int64_t MOD=1000000007;


int main() {

  int n; cin>>n;
  int ans[100005];
  
  rep (x, 105) {
    rep (y, 105) {
      rep (z, 105) {
        ans[x*x + y*y + z*z + x*y + x*z + y*z]++;
      }
    }
  }
  for (int i=1; i<=n; i++) {
    cout<< ans[i] <<endl;
  }
}

### 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;
#define rep(i, n) for (int i = 1; i < (int)(n); i++)
int64_t MOD=1000000007;


int main() {

  int n; cin>>n;
  int ans[100005];
  
  rep (x, 105) {
    rep (y, 105) {
      rep (z, 105) {
        ans[x*x + y*y + z*z + x*y + x*z + y*z]++;
      }
    }
  }
  for (int i=1; i<=n; i++) {
    cout<< ans[i] <<endl;
  }
}

```