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>
#define ll long long
#define rep(i, n) for (ll i = 0; i < (ll)(n); i++)
#define repi(i, a, b) for (ll i = (ll)(a); i < (ll)(b); i++)
#define repm(i, a, b) for (ll i = (ll)(a); i > (ll)(b); i--)
#define all(v) v.begin(), v.end()
#define rall(x) (x).rbegin(), (x).rend()
#define pll pair<long long, long long>
#define pb push_back
#define mp make_pair
#define mt make_tuple
#define vc vector<char>
#define vvc vector<vc>
using namespace std;
using vi = vector<int>;
using vvi = vector<vi>;
using vll = vector<long long>;
using vvll = vector<vll>;
using vb = vector<bool>;
using vvb = vector<vb>;
template <class T>bool chmax(T &a, const T &b){if (a < b){a = b;return 1;}return 0;}
template <class T>bool chmin(T &a, const T &b){if (b < a){a = b;return 1;}return 0;}
//snippets:tmp,cl,cvl,cs,co,coy,con,cov,setp
const ll mod=1e9+7;

int main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    ll n;
    cin >> n;
    vll d(10010,0);
    repi(x,1,101){
        repi(y,1,101){
            repi(z,1,101){
                if(x*x+y*y+z*z+x*y+y*z+z*x<=10000){
                    d[x*x+y*y+z*z+x*y+y*z+z*x]++;
                }
            }
        }
    }
    repi(i,1,n+1){
        cout<<d[i]<<endl;
    }
}