#include <bits/stdc++.h>
using namespace std;
int main(void){
    std::map<int, int> map;
    for (int x=1;x<=100;x++) {
        for (int y=1;y<=100;y++) {
            for (int z=1;z<=100;z++) {
                map[x*x+y*y+z*z+x*y+y*z+z*x]++;
            }
        }
    }
    int n;
    cin>>n;
    for (int i=1;i<=n;i++) {
        cout<<map[i]<<endl;
    }
}

### Prompt

Please create a solution in cpp 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(void){
    std::map<int, int> map;
    for (int x=1;x<=100;x++) {
        for (int y=1;y<=100;y++) {
            for (int z=1;z<=100;z++) {
                map[x*x+y*y+z*z+x*y+y*z+z*x]++;
            }
        }
    }
    int n;
    cin>>n;
    for (int i=1;i<=n;i++) {
        cout<<map[i]<<endl;
    }
}

```