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)

#include <bits/stdc++.h>
using namespace std;
#define endl '\n'
#define ini(a,i) memset(a,i,sizeof(a))
#define pb push_back
#define ll int64_t
#define inf LLONG_MAX

void solve()
{
    ll n,i;
    cin>>n;

    ll arr[100005];
    memset(arr,0,sizeof(arr));

    for(i=1;i<105;i++)    
    {
        for(ll j=1;j<105;j++)    
        {
            for(ll k=1;k<105;k++)    
            {
                ll val = (i*i)+(j*j)+(k*k)+(i*j)+(j*k)+(i*k);
                arr[val]++;
            }
            
        }
        
    }

    for(i=1;i<=n;i++)    {cout<<arr[i]<<endl;}
    
    

}


signed main()
{
    std::ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
    //ll tt;    cin>>tt;    while(tt--)
    {
        solve();
     }
    cerr<<" Execution : "<<(1.0*clock())/CLOCKS_PER_SEC<<"s \n";
        
        
return 0;
}