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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;

namespace atcoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine());
            var max = Math.Sqrt(n);
            var resultDic = new Dictionary<int, int>();

            for (var i = 1; i <= max; i++)
            {
                for (var j = 1; j <= max; j++)
                {
                    for (var k = 1; k <= max; k++)
                    {
                        var num = i * i + j * j + k * k + i * j + i * k + j * k;
                        if (resultDic.TryGetValue(num, out _))
                        {
                            resultDic[num]++;
                        }
                        else
                        {
                            resultDic[num] = 1;
                        }
                    }
                }
            }

            for (var i = 1; i <= n; i++)
            {
                Console.WriteLine(resultDic.TryGetValue(i, out var val) ? val : 0);
            }
        }
    }
}