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 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.*;
public class Main {

	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int a = scan.nextInt();
		
		for(int n = 1; n <= a; n++) {
			int num = 0;
			int count = (int)(Math.sqrt(n)/Math.sqrt(6) + 1);
			for(int x = 1; x <= count; x++) {
				for(int y = x; y <= 3*n; y++) {
					for(int z = y; z <= 3*n; z++) {
						if(x*x + y*y + z*z + x*y + y*z + z*x == n) {
							if(x == y) {
								if(y == z) {
									num++;
								} else {
									num += 3;
								}
							} else if(y == z) {
								num += 3;
							} else if(z == x) {
								num += 3;
							} else {
								num += 6;
							}
						}
					}
				}
			}
			System.out.println(num);
		}
	}

}