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 Lua (Lua 5.3.5) (judge verdict: Time Limit Exceeded)

n = io.read("*n")
for k = 1, n do
  cnt = 0
  for x = 1, math.floor(math.sqrt(k)) do
    for y = 1, x do
      for z = 1, y do
        if (x * x + y * y + z * z + x * y + x * z + y * z) == k then
          if x == y and y == z then
            cnt = cnt + 1
          elseif (x == y and y ~= z) or (x == z and x ~=y) or(y == z and y ~= x) then
            cnt = cnt + 3
          elseif (x ~= y and x ~= z and y ~= z) then
            cnt = cnt + 6
          end
        end
      end
    end
  end
  print(cnt)
end