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

int cnt[100010];

int main()
{
    int x, y, z;
    int N;
    scanf("%d", &N);
    for(x=1; x<=100; ++x){
        for(y=1; y<=100; ++y){
            for(z=1; z<=100; ++z){
                ++cnt[x*x+y*y+z*z+x*y+y*z+z*x];
            }
        }
    }
    for(int i=1; i<=N; ++i) printf("%d\n", cnt[i]);
}
### 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 cnt[100010];

int main()
{
    int x, y, z;
    int N;
    scanf("%d", &N);
    for(x=1; x<=100; ++x){
        for(y=1; y<=100; ++y){
            for(z=1; z<=100; ++z){
                ++cnt[x*x+y*y+z*z+x*y+y*z+z*x];
            }
        }
    }
    for(int i=1; i<=N; ++i) printf("%d\n", cnt[i]);
}
```