Problem:
Score : 300 points

Problem Statement

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).

Sample Input 1

20

Sample Output 1

0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
3
3
0
0

For n=6, only (1,1,1) satisfies both of the conditions. Thus, f(6) = 1.

For n=11, three triples, (1,1,2), (1,2,1), and (2,1,1), satisfy both of the conditions. Thus, f(6) = 3.

For n=17, three triples, (1,2,2), (2,1,2), and (2,2,1), satisfy both of the conditions. Thus, f(17) = 3.

For n=18, three triples, (1,1,3), (1,3,1), and (3,1,1), satisfy both of the conditions. Thus, f(18) = 3.

Solution in C++ (GCC 9.2.1) (judge verdict: Accepted)

///in the name of ALLAH
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
int main()
{
    int n;
    cin>>n;
    ///pre calculate
    int ar[10005];
    int mx=10000;
    memset(ar,0,sizeof(ar));
    for(int i=1;i<=sqrt(n);i++)
    {
        for(int j=1;j<=sqrt(n);j++)
        {
            for(int k=1;k<=sqrt(n);k++)
            {
               ll p=i*i+j*j+k*k+i*j+j*k+k*i;
               if(p<=n)
                    ar[p]++;
            }
        }
    }
    for(int i=1;i<=n;i++)
        cout<<ar[i]<<endl;


}