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)

n = gets.chomp.to_i
a = (1..250).map{|i|i}
combs = a.repeated_combination(3).to_a

def hoge(x,y,z)
  x ** 2 + y ** 2 + z ** 2 + x*y + y*z + z*x
end

hash = {}
combs.each do |c|
  result = hoge(*c)
  if (c[0] == c[1] && c[1] == c[2])
  	hash[result] ? hash[result] += 1 : hash[result] = 1
  else
    hash[result] ? hash[result] += 3 : hash[result] = 3
  end
end

n.times do |i|
  puts hash[i+1] ? hash[i+1] : 0
end