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: Wrong Answer)

import java.util.*;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		sc.close();

		Map<Integer, Integer> map = new TreeMap<Integer, Integer>();

		for (int x = 1; x < 20; x++) {
			for (int y = 1; y < 20; y++) {
				for (int z = 1; z < 20; z++) {
					int num = (x + y + z) * (x + y + z) - (x * y + y * z + z * x);
					if (map.containsKey(num)) {
						map.put(num, map.get(num) + 1);
					} else {
						map.put(num, 1);
					}
				}
			}
		}

		for (int i = 1; i <= N; i++) {
			if (map.containsKey(i)) {
				System.out.println(map.get(i));
			} else {
				System.out.println(0);
			}
		}
	}
}