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 fastio {\
    ios::sync_with_stdio(0);\
    cin.tie(0);\
}

#define file {\
    freopen("io\\in.txt", "r", stdin);\
    freopen("io\\out.txt", "w", stdout);\
    freopen("io\\err.txt", "w", stderr);\
}

#ifdef LOCAL
#define debug(args...) {\
    string _s(#args);\
    replace(_s.begin(), _s.end(), ',', ' ');\
    stringstream _ss(_s);\
    istream_iterator<string> _it(_ss);\
    debug1(_it, args);\
}

#pragma GCC diagnostic ignored "-Wunused-parameter"
void debug1(istream_iterator<string> it) {
    cerr << endl;
}
#pragma GCC diagnostic pop

template<class T, class... Args>
void debug1(istream_iterator<string> it, T a, Args... args) {
    cerr << '>' << *it << " = " << a << "; ";
    debug1(++it, args...);
}
#else
#define debug(args...)
#define cerr if (false) cerr
#endif

using ll = long long;
using vi = vector<int>;
using vvi = vector<vi>;
using si = set<int>;
using ii = pair<int, int>;
using vii = vector<ii>;

#define rep(i, n)   for (int i = 0; i < n; i++)
#define dotc()      int tcs; if (cin >> tcs) rep(tc, tcs)
#define sz(x)       (int)x.size()
#define eb          emplace_back
#define pb          push_back
#define mp          make_pair
#define mt          make_tuple
#define all(x)      x.begin(), x.end()
#define rall(x)     x.rbegin(), x.rend()
#define fi          first
#define se          second

const int inf(0x3fffffff);
const int mod(1000000007);
const double pi(acos(-1.0));

signed main() {
    fastio;
#ifdef LOCAL
    file;
#endif

    int n;
    cin >> n;
    vi a(n + 1);

    for (int i = 1;; i++) {
        if (i * i + 2 + i + 1 + i > n) break;
        for (int j = 1;; j++) {
            if (i * i + j * j + 1 + i * j + i + j > n) break;
            for (int k = 1;; k++) {
                if (i * i + j * j + k * k + i * j + i * k + j * k > n) break;
                a[i * i + j * j + k * k + i * j + i * k + j * k]++;
            }
        }
    }

    for (int i = 1; i <= n; i++) cout << a[i] << '\n';

    return 0;
}