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# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Linq;
using System.Runtime.InteropServices.ComTypes;
using System.Security.Cryptography.X509Certificates;

namespace Aisingcontest2020
{
    class Program
    {
        static void Main(string[] args)
        {
            c();
        }

        public static void c()
        {
            int n = int.Parse(Console.ReadLine());
            for(int i = 1; i <= n; i++)
            {
                int sum = 0;
                bool flg = true;
                for(int j = 1; j <= n; j++)
                {
                    if (j >= 100)
                        break;
                    for(int k = 1; j + k <= n; k++)
                    {
                        if (k >= 100)
                            break;
                        for(int l = 1; j + k + l <= n; l++)
                        {
                            if (l >= 100)
                            {
                                flg = false;
                                break;
                            }
                            if ((j * j) + (k * k) + (l * l) + (j * k) + (k * l) + (j * l) == i)
                                sum++;
                        }
                        if (flg == false)
                            break;
                    }
                    if (flg == false)
                        break;
                }
                Console.WriteLine(sum);
            }
        }
    }
}