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 = sc.nextInt();
        int ans[] = new int [N];
        int count  = 0;
        for (int flg = 1; flg <= N; flg++) {
            double temp = Math.sqrt(flg);
            for (int a = 1; a < temp; a++) {
                for (int b = 1; b < temp; b++) {
                    for (int c = 1; c < temp; c++) {
                        int math = a*a + b*b + c*c + a*b + b*c + c*a;
                        if (math == flg) {
                            ans[flg-1]++;
                        }
                    }
                }
            }
            System.out.println(ans[flg-1]);
        };
    }
}