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 rep(i, a, b) for(int i = a; i < (b); ++i)
#define trav(a, x) for (auto& a : (x))
#define all(x) x.begin(), x.end() // sort(all(x))
#define sz(x) (int)(x).size()
#define mp(x, y) make_pair((x), (y))

typedef long long ll;

typedef double T;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef tuple<int, int, int> tiii;

typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<vi> vvi;
typedef vector<vl> vvl;
typedef vector<T> vt;
typedef vector<vt> vvt;
typedef vector<pii> vpi;
typedef vector<pii> vpl;
typedef vector<vpi> graph;
typedef complex<T> Pt;
typedef pair<Pt, Pt> Line;

const ll MOD = 1e9 + 7; // 998244353;
const T EPS = 1e-10;
const int INF = 1e9 + 1;

/* Mod Library */

struct Mod {
    ll x;
    Mod (ll x = 0) : x(x) {}
    Mod operator+(Mod b) { return Mod((x + b.x)%MOD); }
    Mod operator-(Mod b) { return Mod((x - b.x + MOD)%MOD); }
    Mod operator*(Mod b) { return Mod((x * b.x)%MOD); }
    Mod operator/(Mod b) { return *this * inverse(b); }
    Mod operator%(Mod b) { return Mod(x % b.x); }

    static ll euclid(ll a, ll b, ll &x, ll &y) {
        if (b) {
            ll d = euclid(b, a%b, y, x);
            y -= a/b*x;
            return d;
        }
        x = 1; 
        y = 0;
        return a;
    }
    
    Mod inverse(Mod a) {
        ll x, y, g = euclid(a.x, MOD, x, y);
        assert(g == 1);
        return Mod((x + MOD)%MOD);
    }

    Mod operator^(ll e) {
        if (!e) return Mod(1);
        Mod r = *this^(e/2);
        r = r*r;
        return e&1 ? *this*r : r;
    }
};

/* Input Library */
template <typename A, typename B>
istream& operator>>(istream &in, pair<A, B> &p) {
    in >> p.first >> p.second;
    return in;
}

template <typename A, typename B>
ostream& operator<<(ostream &out, pair<A, B> &p) {
    out << p.first << " " << p.second;
    return out;
}

template <typename I>
istream& operator>>(istream &in, vector<I> &a) {
    trav(i, a) in >> i;
    return in;
}

template <typename I>
ostream& operator<<(ostream &out, vector<I> &a) {
    rep(i, 0, sz(a)) {
        if (i) out << " ";
        out << a[i];
    }
    return out;
}

void fast_io() {
    cin.sync_with_stdio(0);
    cin.tie(0);
    //cout.tie(0);
    cin.exceptions(cin.failbit);
} 

void solve_test() {
  vi ans(10101);
  for (int x = 1; x < 100; ++x) {
    for (int y = 1; y < 100; ++y) {
      for (int z = 1; z < 100; ++z) {
        int n = x*x + y*y + z*z + x*y + x*z + y*z;
        if (n <= 1e4) {
          ans[n]++;
        }
      }
    }
  }

  int n; 
  cin >> n;
  for (int i = 1; i <= n; ++i) {
    cout << ans[i] << endl;
  }
}

void setup() {
}

int main() {
    setup();
    srand(time(0));
    fast_io();
    int t = 1;
    //cin >> t;
    while (t--) {
        solve_test();
    }
}