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: Runtime Error)

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

namespace AtCoder.AISing
{
    class C
    {
        public static void Main()
        {
            var n = int.Parse(Console.ReadLine());
            var count = new int[n + 1];
            var square = Enumerable.Range(0, 200).Select(x => x * x).ToArray();

            var nsqrt = (int)Math.Sqrt(n);

            for (int x = 1; x <= nsqrt; x++)
            {
                for (int y = 1; y <= nsqrt; y++)
                {
                    for (int z = 1; z <= nsqrt; z++)
                    {
                        var a = square[x + y] + square[y + z] + square[z + x];
                        if (2 * n < a || a % 2 == 1)
                            break;
                        count[a/2]++;
                    }
                }
            }
            for (int i = 1; i <= n; i++)
                Console.WriteLine(count[i]);
        }
    }
}