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: Time Limit Exceeded)

#include<bits/stdc++.h>
using namespace std;
#define ll  long long int
#define all(x) x.begin(), x.end()
bool isPowerOfTwo(int n)
{
    return (ceil(log2(n)) == floor(log2(n)));
}


int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    int n;
    cin>>n;
    for(int i=1;i<=n;i++)
    {   int ans=0;
        for(int x=1;x<=sqrt(i);x++)
        {

            for(int y=1;y<=sqrt(i);y++)
            {
                if(x*x+y*y+x*y>i){break;}

                    for(int z=1;z<=sqrt(i);z++){
                    if(x*x+y*y+z*z+x*y+y*z+z*x>i){break;}
                    if(x*x+y*y+z*z+x*y+y*z+z*x==i)
                    {
                        ans++;
                    }
                }
            }

        }
        cout<<ans<<endl;
    }



    return 0;

}