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.*;

public class Main {

  private static void solve(int N) {
    Map<Integer, Integer> map = new HashMap<>();
    for (int x = 1; x <= N; x++) {
      for (int y = 1; y <= N; y++) {
        for (int z = 1; z <= N; z++) {
          int val = x * x + y * y + z * z + x * y + y * z + z * x;
          map.put(val, map.getOrDefault(val, 0) + 1);
        }
      }
    }
    for (int i = 1; i <= N; i++) {
      int res = 0;
      if (map.containsKey(i)) {
        res += map.get(i);
      }
      System.out.println(res);
    }
  }

  public static void main(String[] args) {
    int N = scanner.nextInt();
    solve(N);
  }

  private static final Scanner scanner = new Scanner(System.in);
}