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 Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

import java.util.*;

public class Main
{
    public static void main(String[] args)
    {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();

        for (int i = 1;i<=n;++i)
        {
            int r = (int)Math.sqrt(i);
            int max = Math.pow(r,2)+r+r <= i ? r:r-1;
            //System.err.println("@"+i+" max = "+max);
            int count = 0;
            for (int x = 1;x<=max;++x)
            {
                for (int y = 1;y<=max;++y)
                {
                    for (int z = 1;z<=max;++z)
                    {
                        int sum = 0;
                        sum += (int) Math.pow(x,2) + (int) Math.pow(y,2) + (int) Math.pow(z,2)
                                + x*y + y*z + x*z;
                        if (sum == i) ++count;
                    }
                }
            }
            //System.err.println(i+":"+count);
            System.out.println(count);
        }
        sc.close();
    }
}