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 <iostream>
#include <math.h>
#include <cmath>

using namespace std;

int out[10005] = {};

int main() {
  for (int x=1; x < 100; x++) {
    for (int y=1; y < 100; y++) {
      for (int z=1; z < 100; z++) {
        int idx = (x*x) + (y*y) + (z*z) + (x*y) + (y*z) + (z*x);
        if (10004 >= idx) {
          if (out[idx]!=0) continue;
          if (x==y && y==z && z==x) out[idx] = 1;
          else if(x==y || y==z || z==x) out[idx] = 3;
          else out[idx] = 6;
        }
      }
    }
  }
  int N; cin >> N;
  for (int i=1; i <= N; i++) cout << out[i] << endl;

  return 0;
}