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
ans = Array.new(10**4 + 1, 0)
## x <= y <= zとする。
max_x = Math.sqrt(n/6).to_i
max_y = Math.sqrt(n/3).to_i
max_z = Math.sqrt(n).to_i
(1..max_x).each do |x|
  (x..max_y).each do |y|
    break if x**2 + y**2 + x*y + x + y + 1 > n
    (y..max_z).each do |z|
      result = x**2 + y**2 + z**2 + x*y + y*z + z*x
	  break if result > n
      if x == y && x == z
	      plus_cnt = 1
      elsif x == y || y == z || z == x
          plus_cnt = 3
      else
          plus_cnt = 6
      end
	      ans[result] += plus_cnt if result <= n
    end
  end
end
(1..n).each do |i|
  puts ans[i]
end