$4)$ Consider the scenario given below and solve the problem with using any algorithms provided in constraint satisfaction problems $($CSP$)$ class. Show each step and the problem formulation with CSP algorithms.

You are asked to find a solution for class scheduling problem. You will schedule the courses into $3$ days only $($Let$\text{'}$s assume Monday, Tuesday and Wednesday$),$ you have one classroom to schedule, and one professor can teach one class at a time $($Can give multiple classes in different days, but can not teach simultaneously$).$ You have $5$ courses and $3$ professors with below conditions.

Course $1-$ Intro to Java: between $15$:$00-16$:$00$

Course $2-$ Intro to Artificial Intelligence: between $15$:$30-16$:$30$

Course $3-$ Natural Language Processing: between $16$:$00-17$:$00$

Course $4-$ Mobile Programming: between $16$:$00-17$:$00$

Course $5-$ Machine Learning: between $16$:$30-17$:$30$

Professor A$,$ can teach Classes $3$ and $4$

Professor B$,$ can teach Classes $2,3,4,5$

Professor C$,$ can teach Classes $1,2,3,4,5$