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 <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
using namespace std;
int trip(int n)
{
	int x,y,z,num=0;
	for (x=1;x<=sqrt(n);x++)
	{
		for (y=1;y<=sqrt(n);y++)
		{
			for (z=1;z<sqrt(n);z++)
			{
				if (x*x+y*y+z*z+x*y+y*z+x*z==n) num++;
			}
		}
	}
	return num;
}

int main()
{
    int n;
    scanf("%d",&n);
    for (int i=1;i<=n;i++)
    {
    	printf("%d\n",trip(i));
	}
    return 0;
}