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)

input = readlines()
n = input.shift.chomp.to_i

r_hash = {}
(1..n).each do |x|
  (1..n).each do |y|
    break if y > x
    (1..n).each do |z|
      break if z > y
      r = x*x + y*y + z*z + x*y + y*z + z*x
      break if r > n
      r_hash[r] = [] if r_hash[r].nil?
      r_hash[r].push([x,y,z])
    end
  end
end

(1..n).each do |num|
  cnt = 0
  r_hash[num].to_a.each do |r|
    cnt += 1 if r.uniq.length == 1
    cnt += 3 if r.uniq.length == 2
    cnt += 6 if r.uniq.length == 3
  end
  puts cnt
end