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.Scanner;

public class Main{

	public static void main(String[] args) {


		Scanner scanner = new Scanner(System.in);

		int n    = Integer.parseInt(scanner.nextLine());
		int max  = 50;
		int hos  = (max * max)*6 + 1;
		int[] list = new int[hos];
		int now  = 0;
		for(int i = 1; i < max - 1; i++) {
			for(int j = i + 1; j < max; j++) {
				for(int k = j + 1; k < max + 1; k++) {

					now = i * i + j * j + k * k + i * j + i * k + j * k;
					list[now] += 6;

				}
			}
		}

		for(int i = 1; i < max; i++) {
			for(int j = i + 1; j < max + 1; j++) {

				now = (i * i) * 3 + (j * j) + (i * j)*2;
				list[now] += 3;

				now = (j * j) * 3 + (i * i) + (i * j)*2;
				list[now] += 3;

			}
		}

		for(int i = 1; i < max + 1; i++) {

			now = (i * i)*3*2;
			list[now] ++;

		}

		for(int i = 1; i < n + 1; i++) {

			System.out.println(list[i]);
		}


	}

}