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;
using ll = long long;

int main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);

  int n;
  cin >> n;

  map<int, int> ans;

  for (int x = 1; x <= 100; x++) {
    for (int y = x; y <= 100; y++) {
      for (int z = y; z <= 100; z++) {
        ll nn = x * x + y * y + z * z + x * y + y * z + z * x;
        if (nn > n)
          break;
        if (x == y && y == z) {
          ans[nn]++;
        } else if (x == y || y == z) {
          ans[nn] += 3;
        } else {
          ans[nn] += 6;
        }
      }
    }
  }

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

  return 0;
}