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.to_i

cnt = Hash.new { 0 }

finish = false

1.upto(N) do |x|
  x.upto(N) do |y|
    y.upto(N) do |z|
      num = x**2 + y**2 + z**2 + x*y + y*z + z*x

      if num > 10000
        finish = true
        break
      end
      case
      when x == y && y == z then cnt[num] += 1
      when x == y || y == z then cnt[num] += 3
      when x < y && y < z   then cnt[num] += 6
      end
    end

    break if finish
  end
  break if finish
end

1.upto(N) do |i|
  puts cnt[i]
end