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 11.0.6) (judge verdict: Time Limit Exceeded)

import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		try(Scanner scanner = new Scanner(System.in)) {
			String data = scanner.nextLine();

			int N = Integer.parseInt(data);

			for (int i = 1; i <= N; i++) {
				System.out.println(count(i));
			}
		}
	}

	private static int count(int n) {
		int count = 0;
		for (int x = 1; x <= n/2; x++) {
			if ((x * x) >= n) {
				continue;
			}
			for (int y = 1; y <= n/2; y++) {
				if ((y * y) >= n || (x * y) >= n) {
					continue;
				}
				for (int z = 1; z <= n/2; z++) {
					 if ((z * z) >= n || (z * x) >= n || (y * z) >= n) {
						continue;
					}

					if (calc(x, y, z) == n) {
						count++;
					}
				}
			}
		}
		return count;
	}

	private static long calc(int x, int y, int z) {
		return (x * x) + (y * y) + (z * z) + (x * y) + (y * z) + (z * x);
	}
}