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 Java (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		int Y = 1;
		int Z = 1;
		List<Integer> list = new ArrayList<Integer>();
		for (int i = 1; i <= n; i++) {
			int count = 0;
			for (int x = 1;; x++) {
				if (cal(x, Y, Z) > i) {
					break;
				}
				for (int y = 1;; y++) {
					if (cal(x, y, Z) > i) {
						break;
					}
					for (int z = 1;; z++) {
						if (cal(x, y, z) > i) {
							break;
						} else if (cal(x, y, z) == i) {
							count++;
						}
					}
				}
			}
			list.add(count);
		}
		for (int i : list) {
			System.out.println(i);
		}
	}

	public static int cal(int x, int y, int z) {
		return (int) (Math.pow(x, 2) + Math.pow(y, 2) + Math.pow(z, 2) + x * y + y * z + z * x);
	}

}