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: Wrong Answer)

num = gets.to_i

nums = []
oks = {}

for x in 1..num do
  for y in 1..num do
    for z in 1..num do
      unless nums.include?(x + y + z)
        nums << x + y + z
        for n in 1..num do
          result = (x*x) + (y*y) + (z*z) + (x*y) + (y*z) + (z*x)
          if result == n
            oks[n] = [x,y,z]
          end
        end
      end
    end
  end
end

for n in 1..num do
  if oks[n].nil?
    puts 0
    next
  end

  if oks[n].uniq.size == 1
    puts 1
  elsif oks[n].uniq.size == 2
    puts 3
  else oks[n].uniq.size ==  3
    puts 6
  end
end