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)

n = gets.chomp.to_i
h = {}

1.upto(100) do |x|
  x.upto(100) do |y|
    y.upto(100) do |z|
      tmp = x * x + y * y + z * z + x * y + y * z + z * x

      h[tmp] ||= []
      h[tmp] << [x, y, z]
    end
  end
end

def count(arr)
  ret = 0
  arr.each do |(x, y, z)|
    if x == y && y == z
      ret += 1
    elsif x == y || y == z
      ret += 3
    else
      ret += 6
    end
  end
  ret
end

1.upto(n) do |m|
  unless h[m]
    puts 0
    next
  end

  cnt = count(h[m])
  puts cnt
end