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) {
		int ans=0;
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		//int hako[]=new int[n];
		/*for(int i=1;i<=n;i++) {
			hako[i]=sc.nextInt();
		}*/
		for(int i=1;i<=n;i++) {
			s:for(int x=1;x<=i;x++) {
				for(int y=1;y<=i;y++) {
					for(int z=1;z<=i;z++) {
						if((x*x)+(y*y)+(z*z)+(x*y)+(y*z)+(z*x)==i && x==y && y==z && z==x) {
							System.out.println(1);
							break s;
						}
						else if((x*x)+(y*y)+(z*z)+(x*y)+(y*z)+(z*x)==i) {
							System.out.println(3);
							break s;
						}
						else if((x*x)+(y*y)+(z*z)+(x*y)+(y*z)+(z*x)>i && y==i) {
							System.out.println(0);
							break s;
						}
					}
				}
			}
		}
		
		
	}
}