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

int main(){
int n;
cin >> n;
map<int, int> mp;
for(int i = 1; i<=100;i++){
  for(int j= 1; j<=100; j++){
    for(int k = 1; k<=100; k++){
          ll m = i*i+j*j+k*k+i*j+j*k+k*i;
         mp[m]++;
       }
    }
}
for(int i=1; i<=n; i++)cout << mp[i] << endl;
return 0;
}
### Prompt

Please provide a Cpp coded solution to the problem described below:

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;
using ll = long long;

int main(){
int n;
cin >> n;
map<int, int> mp;
for(int i = 1; i<=100;i++){
  for(int j= 1; j<=100; j++){
    for(int k = 1; k<=100; k++){
          ll m = i*i+j*j+k*k+i*j+j*k+k*i;
         mp[m]++;
       }
    }
}
for(int i=1; i<=n; i++)cout << mp[i] << endl;
return 0;
}
```