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: Accepted)

open Printf
open Scanf

let id x = x
exception Break

let n = scanf "%d"id

let int_sqrt n = truncate (sqrt (float n))

let run () =
    let nn = Array.init (n + 1) (fun _ -> ref 0) in
    let max = int_sqrt n in
    begin
        try for x = 1 to max do
            try for y = 1 to max do
                try for z = 1 to max do
                    let i = x * x + y * y + z * z + x * y + y * z + z * x in
                    if i > n then begin
                        raise Break
                    end else incr (nn.(i))
                done with Break -> ()
            done with Break -> ()
        done with Break -> ()
    end;
    for i = 1 to n do
        printf "%d\n" !(nn.(i))
    done
    
let () = run ()