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)

object Main extends App {
  val inputs: Seq[String] = scala.io.Source.stdin.getLines().toList
  val n    = inputs(0).toInt

  solve(n)

  def solve(n: Int): Unit = {
    var nMap = scala.collection.mutable.HashMap.empty[Long, Int]

    (1L to 100L).foreach { i =>
      (1L to 100L).foreach { j =>
        (1L to 100L).foreach { k =>
          val f = i*i + j*j + k*k + i*j + j*k + k*i
          nMap.update(f, nMap.applyOrElse(f, (k: Long) => 0) + 1)
        }
      }
    }
    (1 to n).foreach { i =>
      println(nMap.applyOrElse(i.toLong, (k: Long) => 0))
    }
  }
}