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<bits/stdc++.h>
#define ll 	long long
#define pb push_back
using namespace std;
#define pi acos(-1.0)

int main()
{

ll a[10004];

 ll n;
 cin>>n;
 
  for(ll x=1;x<=150;x++)
  {
    for(ll y=1;y<=150;y++)
    {
      for(ll z=1;z<=150;z++)
      {
        ll tt = x*x +y*y+z*z+x*y+y*z+z*x;
        if(tt>n)
		continue;
        a[tt]++;
      }
    }
  }
  for(ll i=1;i<=n;i++)
  cout<<a[i]<<endl;

    
    return 0;
}