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 sqr(x) ((x)*(x))
#define cube(x) ((x)*(x)*(x))
#define GCD(a, b) (__gcd(a, b))
#define LCM(a, b) ((a)/GCD(a,b)*(b))
#define PI (3.14159265358979323846)
#define MP make_pair
#define n1 first
#define n2 second
#define ALL(x) (x).begin(), (x).end()
#define PII pair<int,int>
#define PLL pair<ll,ll>
#define PDB pair<db,db>
#define SI set<int>
#define SL set<ll>
#define MS multiset
#define MSI multiset<int>
#define MSLL multiset<ll>
#define PB push_back
#define PF push_front
#define VI vector<int>
#define VPI vector<pair<int,int>>
#define VLL vector<ll>
#define VS vector<string>
#define SZ(x) ((int)x.size())

typedef long long ll;

typedef unsigned long long ull;
typedef long double ld;
typedef double db;
const db eps = 0.000001;
const int INF = 1000000007;
const ll LINF = 1000000000000000555;
const int N = 1550555;
const int M = 5125;

int cnt[N];
void solve() {
    int n;
    cin >> n;

    for (int x = 1; x <= 100; x++){
        for (int y = 1; y <= 100; y++){
            for (int z = 1; z <= 100; z++){
                int k = x*x + y*y + z*z + x*y + y*z + x*z;
                cnt[k]++;
            }
        }
    }

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

}

int main() {
    ios_base::sync_with_stdio(false);
#ifdef dxz05
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
#else

#endif

    int T = 1;
    //cin >> T;

    while (T--) {
        solve();
    }

    return 0;
}