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: Accepted)

import java.util.HashSet;
import java.util.Scanner;

public class Main {
    public static void main(String... args) {
        Scanner scanner = new Scanner(System.in);

        int N = scanner.nextInt();
        int sqrtN = (int) Math.floor(Math.sqrt(N));
        int[] cnt = new int[N];


        for (int x = 1; x < sqrtN; x++) {
            for (int y = 1; y < sqrtN; y++) {
                for (int z = 1; z < sqrtN; z++) {
                    int n = x * x +
                            y * y +
                            z * z +
                            x * y +
                            y * z +
                            z * x;

                    if (n > cnt.length) continue;
                    cnt[n - 1]++;
                }
            }
        }

        for (int i = 0; i < N; i++) {
            System.out.println(cnt[i]);
        }
    }
}