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 }

1.upto(N) do |n|
  num = n ** 2 * 6
  cnt[num] += 1
end

catch(:done) do
  1.upto(N) do |x|
    (x+1).upto(N) do |y|
      num = x**2 + y**2 * 3 + x * y * 2

      throw :done if num > 10000

      cnt[num] += 3
    end
  end
end

catch(:done) do
  1.upto(N) do |y|
    (y+1).upto(N) do |x|
      num = x**2 + y**2 * 3 + x * y * 2

      throw :done if num > 10000

      cnt[num] += 3
    end
  end
end

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

        throw :done if num > 10000

        cnt[num] += 6
      end
    end
  end
end

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