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 Ruby (2.7.1) (judge verdict: Accepted)

class XYZ_Triplets
  def initialize(n)
    @n = n
    @ac = Array.new(n+1, 0)
    @ls = (1..).take_while{|i| i * i < n}
  end

  def solve
    @ls.each do |x|
      @ls.each do |y|
        @ls.each do |z|
          m = x * x + y * y + z * z + x * y + y * z + z * x
          if m <= @n
            @ac[m] += 1
          end
        end
      end
    end
    
    (1..@n).each do |i|
      puts @ac[i]
    end
  end
end

def run
  n = gets.chomp.to_i
  
  XYZ_Triplets.new(n).solve
end

run