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: Time Limit Exceeded)

def f(x,y,z)
  return x**2 + y**2 + z**2 + x*y + y*z + z*x
  
end
def check(x=1,y=1,z=1,n)
  [0,1].repeated_combinataion(3) do |x,y,z|
  end
end

def fact(x)
  case x
    when 3
      return 6
    when 2
      return 2
    when 1
      return 1
  end
end

def check(n)
  cnt = 0
  1.upto(100) do |x|
    break if f(x, 1, 1) > n
    1.upto(100) do |y|
      break if f(x, y, 1) > n
      1.upto(100) do |z|
        if f(x,y,z) == n
          arr=[x,y,z]
          cnt += 1
        else
          if f(x,y,z) > n
            break
          end
        end
      end
    end
  end
  return cnt
end

N = gets.to_i
1.upto(N) do |i|
  puts check(i)
end