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;
import java.lang.Math;

public class Main {
  public static void main(String[] args) {
    Scanner scan = new Scanner(System.in);
    String str = scan.nextLine();
    var N = Integer.parseInt(str);
    int ans = 0;
    double x,y,z;
    int a;
    double b;

    for (var i = 1;i <= N;i++) {
      ans = 0;
      a = (int)Math.sqrt(N);

      for (x = 1; x <= a; x++){
        for (y = 1; y <= a; y++){
          for (z = 1; z <= a; z++){
	     b = Math.pow(x,2)+Math.pow(y,2)+Math.pow(z,2)+(x*y)+(y*z)+(z*x);
	     if( (int)b == i ){
		     ans++;
	     }
	  }
	}
      }


      System.out.println(ans);
    }

    scan.close();
  }
}