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 <vector>
using namespace std;

int g(int x, int y, int z){
  int k = x + y + z;
 return k*k-x*y-y*z-z*x;
}

int main(void){
  int N;
  cin>>N;
  vector<int> ans(N,0);
  int a0=6;
  int n0=5;
  int k=3;
  while(a0<=N){
    for(int x=1;x<=k-2;x++){
      for(int y=1;y<k-x;y++){
      	ans[g(x,y,k-x-y)-1]++;
      }
    }
    a0+=n0;
    n0+=2;
    k++;
  }
  for(int i=0;i<N;i++)cout<<ans[i]<<endl;
  return 0; 
}