// Textbook fragment 10.11
  public Entry<K,V> remove(Entry<K,V> ent) throws InvalidEntryException {
    Entry<K,V> toReturn = super.remove(ent);
    Position<Entry<K,V>> posR = actionPos;
    if (toReturn != null) {
      if (wasParentRed(posR) || isRoot(posR) || isPosRed(posR))
        setBlack(posR);
      else
        remedyDoubleBlack(posR);
    }
    return toReturn;
  }
  protected void remedyDoubleBlack(Position<Entry<K,V>> posR) {
    Position<Entry<K,V>> posX, posY, posZ;
    boolean oldColor;
    posX = parent(posR);
    posY = sibling(posR);
    if (!isPosRed(posY))  {
      posZ = redChild(posY);
      if (hasRedChild(posY))  { // Case 1: trinode restructuring
        oldColor = isPosRed(posX);
        posZ = restructure(posZ);
        setColor(posZ, oldColor);
        setBlack(posR);
        setBlack(left(posZ));
        setBlack(right(posZ));
        return;
      }
      setBlack(posR);
      setRed(posY);
      if (!isPosRed(posX))  { // Case 2: recoloring
        if (!isRoot(posX))
          remedyDoubleBlack(posX);
        return;
      }
      setBlack(posX);
      return;
    } // Case 3: adjustment
    if (posY == right(posX)) posZ = right(posY);
    else posZ = left(posY);
    restructure(posZ);
    setBlack(posY);
    setRed(posX);
    remedyDoubleBlack(posR);
  }