class Point(p: (Int, Int)) extends Comparable[Point] {

  val _hashCode = 31 * x + y

  /**
   * @return the X coordinate of this Point
   */
  def x: Int = p._1

  /**
   * @return the Y coordinate of this Point
   */
  def y: Int = p._2

  def +(p: (Int, Int)) = Point(x + p._1, y + p._2)

  def +(p: Point) = Point(x + p.x, y + p.y)

  def -(p: (Int, Int)) = Point(x - p._1, y - p._2)

  def -(p: Point) = Point(x - p.x, y - p.y)

  def *(p: (Int, Int)) = Point(x * p._1, y * p._2)

  def *(p: Point) = Point(x * p.x, y * p.y)

  def /(p: (Int, Int)) = Point(x / p._1, y / p._2)

  def /(p: Point) = Point(x / p.x, y / p.y)

  /**
   * @return the magnitude (length) of this point
   */
  def mag = {
    math.sqrt(magSq)
  }

  /**
   * @return the squared magnitude (length) of this point
   */
  def magSq = {
    x * x + y * y
  }

  /**
   * The distance between this point and the given coordinates
   * @param x the X coordinate to calculate the distance to
   * @param y the Y coordinate to calculate the distance to
   * @return the distance between this point and the given coordinates
   *         (this - (x, y)).mag
   */
  def distance(x: Int, y: Int) = {
    (this -(x, y)).mag
  }

  /**
   * The distance between this point and the given coordinates
   * @param p the coordinates to calculate the distance to
   * @return the distance between this point and the given coordinates
   *         (this - coords).mag
   */
  def distance(p: (Int, Int)) = {
    (this - p).mag
  }

  /**
   * The distance between this point and the given coordinates
   * @param p the coordinates to calculate the distance to
   * @return the distance between this point and the given coordinates
   *         (this - p).mag
   */
  def distance(p: Point) = {
    (this - p).mag
  }

  /**
   * The squared distance between this point and the given coordinates
   * @param x the X coordinate to calculate the distance to
   * @param y the Y coordinate to calculate the distance to
   * @return the squared distance between this point and the given coordinates
   *         (this - (x, y)).magSq
   */
  def distanceSq(x: Int, y: Int) = {
    (this -(x, y)).magSq
  }

  /**
   * The squared distance between this point and the given coordinates
   * @param p the coordinates to calculate the distance to
   * @return the squared distance between this point and the given coordinates
   *         (this - p).magSq
   */
  def distanceSq(p: (Int, Int)) = {
    (this - p).magSq
  }

  /**
   * The squared distance between this point and the given coordinates
   * @param p the coordinates to calculate the distance to
   * @return the squared distance between this point and the given coordinates
   *         (this - p).magSq
   */
  def distanceSq(p: Point) = {
    (this - p).magSq
  }

  override def hashCode(): Int = _hashCode

  override def equals(obj: scala.Any): Boolean = {
    obj match {
      case p: Point => return p.x == x && p.y == y
      case (pX, pY) => return pX == x && pY == y
    }
    false
  }

  override def toString = "( " + x + ", " + y + " )"

  override def compareTo(o: Point): Int = {
    if (x != o.x) return if (x < o.x) 1 else -1
    if (y != o.y) return if (y < o.y) 1 else -1
    0
  }
}