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: Runtime Error)

#include <bits/stdc++.h>
using namespace std;

int proc(int x, int y, int z)
{
    return x*x + y*y + z*z + x*y + y*z + z*x;
}

int main() 
{
    int N;
    cin >> N;

    vector<int> a(N);
    for (int x = 1; x < 105; x++) {
        for (int y = x; y < 105; y++) {
            for (int z = y; z < 105; z++) {
                int r = proc(x,y,z);
                // if (r > N) break;
                a[r] += (x == z ? 1 : 3); 
                // a[r] += 1;
            }
        }
    }

    for (int i = 1; i <= N; i++) {
     cout << a[i] << endl;
    }
  
    return 0;
}