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.Configuration;
using System.Linq;

static class Program
{
    static void Main(string[] args)
    {
        var n = int.Parse(Console.ReadLine());
        var s = new int[] { 1, 1, 1 };
        var d = new Dictionary<int, int>();
        int num;
        var kl = new List<int>();
        while (true) {
            num = (int)(Math.Pow(s.Sum(), 2) - s[0] * s[1] - s[1] * s[2] - s[2] * s[0]);
            if (num > n) break;
            var c = (s[0] == s[1] && s[1] == s[2]) ? 1 : 3;
            d.Add(num, c);
            kl.Add(num);
            if (s[0] == s[1]) {
                s[1] = 1;
                s[0]++;
            }
            else {
                s[1]++;
            }
        }
        var k = 0;
        for (var i = 1; n >= i; i++) {
            if (kl[k] != i) Console.WriteLine(0);
            else {
                Console.WriteLine(d[kl[k]]);
                k++;
                if (kl.Count == k) k--;
            }
        }
    }
}