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: Time Limit Exceeded)

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

namespace ABC
{
    class ProgramC
    {
        static void Main(string[] args)
        {
            var n = long.Parse(Console.ReadLine());
            for (var i = 1; i <= n; i++)
            {
                Console.WriteLine(F(i));
            }
        }

        static int F(int n)
        {
            var result = 0;
            // var end = Math.Sqrt(n);
            // 最大値固定版
            var end = 100;
            // Console.WriteLine(string.Format("n: {0}, end: {1}", n, end));

            for (var i = 1; i < end; i++)
            {
                var ii = i * i;
                for (var j = 1; j < end; j++)
                {
                    var jj = j * j;
                    var ij = i * j;
                    for (var k = 1; k < end; k++)
                    {
                        var kk = k * k;
                        var r = ii + jj + kk + ij + i * k + j * k;

                        if (r == n)
                        {
                            result++;
                        }
                        if (r >= n)
                        {
                            break;
                        }
                    }
                }
            }
            return result;
        }
    }
}