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) {
		Scanner sc = new Scanner(System.in);
		int N = Integer.parseInt(sc.next());
		//上限値検索
		for (int i = 1; i <= N; i++) {
			int n = i;
			int max = (int) Math.floor(Math.sqrt((double) n));
			int check = 0;
			for (int s = 1; s <= max; s++) {
				for (int t = 1; t <= max; t++) {
					for (int u = 1; u <= max; u++) {
						if(s * s + t * t + u * u + s * t + t * u + u * s > n) {
							break;
						}
						if (s >= t && t >= u && s * s + t * t + u * u + s * t + t * u + u * s == n) {
							if (s != t & t != u && u != s) {
								check += 6;
							} else if (s == t && t == u && u == s) {
								check++;
							} else {
								check += 3;
							}
						}
					}
				}
			}
			System.out.println(check);
		}
	}

}