Make an E$-$R Diagram that satisfies the $3$rd Normal Form given the following:

$1.$ Each student has a SID, a name and an address.

$2.$ A professor has a PID, a name, and belongs to a department. The age of a professor can be one of "old", "very old", and "still alive."

$3.$ Each course has a number, a name, a credit hour number, an offering department, a classroom, a maximum enrollment, and an actual enrollment.

$4.$ The actual enrollment must be no more than the maximum enrollment.

$5.$ Each department has an ID and a unique name.

$6.$ Each student enrolls in a certain number of courses in this semester.

$7.$ Each course, after assigned, is fully handled by one professor only.

$8.$ A course can have multiple pre$-$requisites. A course can be a pre$-$requisite for multiple other courses. However, a course cannot be a pre$-$requisite for itself.

$9.$ A student enrolled in a course must have enrolled in all pre$-$requisites.

$10.$ More than one professor can teach a course.