#include<bits/stdc++.h>
using namespace std;
const int N=1e4+5;
int f[N];
int main()
{
    int ans=0;
    int n;scanf("%d",&n);
    for(int i=1;i*i<=n;i++)
        for(int j=1;i*i+j*j<=n;j++)
        for(int k=1;k*k+i*i+j*j<=n;k++)
    {
        int s=i*i+j*j+k*k+i*j+i*k+k*j;
        if(s<=n) f[s]++;
    }
    for(int i=1;i<=n;i++) printf("%d\n",f[i]);
}

### Prompt

Your challenge is to write 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;
const int N=1e4+5;
int f[N];
int main()
{
    int ans=0;
    int n;scanf("%d",&n);
    for(int i=1;i*i<=n;i++)
        for(int j=1;i*i+j*j<=n;j++)
        for(int k=1;k*k+i*i+j*j<=n;k++)
    {
        int s=i*i+j*j+k*k+i*j+i*k+k*j;
        if(s<=n) f[s]++;
    }
    for(int i=1;i<=n;i++) printf("%d\n",f[i]);
}

```