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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
using vi = vector<int>;
using vc = vector<char>;
using vs = vector<string>;
using vvi = vector<vector<int>>;
using vvc = vector<vector<char>>;

int main()
{
    int N;
    cin >> N;
    vi f(N+1,0);

    for (int i = 1; i <= N; i++)
    {
        for (int j = 1; j <= 33; j++)
        {
            for (int k = 1; k <= 33-j; k++)
            {
                for (int l = 1; l <= 33-j-k; l++)
                {
                    if(j*j+k*k+l*l+j*k+k*l+l*j==i)f[i]++;
                }   
            }   
        }
    }
    
    
    for (int i = 1; i <= N; i++)
    {
        cout << f[i] << endl;
    }
    
    return 0;
}