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)

n = gets.to_i
c = 0
for i in 1..n
  c = 0
  max = i/3
  for t in 1..max
    x = t
    if c != 0
      break
    end
    for q in 1..i/3+3-t
      y = q
      if c != 0
        break
      end
      for r in 1..i/3+3-(t+q)
        z = r
        ch = x*x + y*y + z*z + x*y + y*z + z*x
        if i == ch
          if x == y && y == z
            c = 1
            break
          elsif x == y || y == z || z == x
            c += 3
            break
          else
            c += 9
            break
          end
        elsif i < ch
          break
        end
      end
    end
  end
  puts c
end