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 rep(i, a, n) for(int i = a; i < n; i++)
using namespace std;
using ll = long long;
using P = pair<int, int>;

int main()
{
    ll n;
    cin >> n;
    int ans = 0;
    rep(i, 0, n){
        ans = 0;
        for(ll x = 1; x*x <= i+1; x++){
            for(ll y = 1; x*x + y*y + x*y <= i+1; y++){
                for(ll z = 1; x*x + y*y + z*z + x*y + y*z + z*x <= i+1; z++){
                    if(x*x + y*y + z*z + x*y + y*z + z*x == i+1) ans++;
                }
            }
        }
        cout << ans << endl;
    }
    return 0;
}