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: Accepted)

#include <iostream>

using namespace std;

int main()
{
    int n;
    cin>>n;
    int arr[10001] = {0};
    int m =  min(n,99);
    for(int i = 1 ; i <= m ; i++)
    {
        for(int j = 1 ; j <= m ;j++)
        {
            for(int z = 1 ; z <= m ;z++)
            {
                if(i*i+j*j+z*z+i*j+i*z+j*z <= 10000)
                    arr[i*i+j*j+z*z+i*j+i*z+j*z]++;
            }
        }
    }
    for(int  i = 1 ; i <= n ; i++)
    {
        cout<<arr[i]<<endl;
    }
    return 0;
}