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# (Mono-mcs 6.8.0.105) (judge verdict: Accepted)

using System;
using System.Collections;
using System.IO;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using System.Collections.Generic;
using System.Threading.Tasks;

class Program
{
	//Main
	static void Main(string[] args)
	{
		//読み込む
		string S = Console.ReadLine();
		int N = int.Parse(S);

		//バケツを用意
		int[] bucket = new int[N];

		//ループ計算（それぞれ高々10^2までで大丈夫）
		for(int i=1; i<=100; i++){
			for(int j=1; j<=100; j++){
				for(int k=1; k<=100; k++){
					int prod = i*i +  j*j + k*k + i*j + j*k + k*i;
					int idx = prod - 1;
					if(idx >= N){
						break;
					}
					else{
						bucket[idx]++;
					}
				}
			}
		}

		//出力
		//出力準備（AutoFlushを切る）
		var sw = new StreamWriter(Console.OpenStandardOutput()){AutoFlush = false};
		Console.SetOut(sw);

		/*
		出力処理の開始
		*/
		foreach(int ans in bucket){
			Console.WriteLine(ans);
		}
		/*
		出力処理の完了
		*/

		//出力終了
		Console.Out.Flush();
	}
}