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.to_i
arr = Array.new(N, 0)

max = Math.sqrt(N).to_i
x, y, z = 1, 1, 1
while z < max do
  n = x ** 2 + y ** 2 + z ** 2 + x * y + y * z + z * x
  if x == y && y == z # 3つとも同じ
    count = 1
  elsif x != y && y != z && z != x # 3つとも異なる
    count = 6
  else
    count = 3
  end
  
  arr[n - 1] += count if n <= N

  # 進める
  x += 1
  if x > max
    y += 1
    x = y
  end
  if y > max
    z += 1
    y, x = z, z
  end
end

puts arr