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 Scala (2.13.1) (judge verdict: Accepted)

import scala.io.StdIn._

object Main extends App {


  val n = readInt()

  def solve() = {
    val lim = 100
    val s = for {
      x <- 1 to lim
      y <- 1 to lim
      z <- 1 to lim
    } yield {
      x*x + y*y + z*z + x*y + y*z + z*x
    }
    val default = Map.empty[Int, Int]
    val numAndCntMap = s.foldLeft(default) { (acc, num) =>
      acc.updated(num, acc.getOrElse(num, 0)+1)
    }
    (1 to n).map { i =>
      numAndCntMap.getOrElse(i, 0)
    }.mkString("\n")
  }

  println(solve())

}