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 OCaml (4.10.0) (judge verdict: Wrong Answer)

let n = Scanf.sscanf (read_line ()) "%d" @@ fun n -> n

let arr = Array.make 10001 0

let () =
  for i = 1 to 50 do
    for j = 1 to 50 do
      for k = 1 to 50 do
        let t = i * i + j * j + k * k + i * j + j * k + k * i in
        if t <= 10000 then arr.(t - 1) <- arr.(t - 1) + 1;
      done
    done
  done;
  for i = 1 to n do
    Printf.printf "%d\n" arr.(i - 1)
  done