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> 
using namespace std;
int main()
{
  int N;
  cin>>N;
  int x;
  int freqarr[10001];
  for(int i=1;i<=sqrt(N);i++){
    for(int j=1;j<=sqrt(N);j++){
      for(int k=1;k<=sqrt(N);k++){
        x=(i*i) +(j*j) +(k*k)+ (i*j)+ (j*k)+ (i*k);
        if(x<=N){
          freqarr[x]++;
        }
        else{
          break;
        }
      }
      
    }
  }
  for(int i=1;i<=N;i++){
    cout<<freqarr[i]<<endl;
  }
  return 0;
}