Question $3$: Synchronization $(30$ points$)$

$($This question is related to ILO $2$c $-$ "explain the underlying causes of concurrency and deadlock issues".$)$

There is a high rating burger store near HKU. This store only serves takeaway with a chef stationed in the store. There is a limited number of chairs for customers to wait for their orders. The interaction and behavior between customers and the chef are as follows:

$-$ If there are no customers waiting, the chef switches off the stove and waits for a customer.

$-$ When a customer arrives and finds an available seat, the customer sits down and waits for their burger.

$-$ If all chairs are occupied, the customer goes away.

$-$ When the chef notices there are waiting customers, the chef fires up the stove if it is not already on$,$ prepares the burger, then places it on the front bench, and informs a customer to pick it up$.$

$-$ The customer gets the burger and leaves the store.

Implement a solution to this problem using condition variables and mutex variables only. You can use the following variables and functions:

$-$ N $-$ the number of chairs

$-$ stove $-$ the state of the stove

$-$ prepare$\_$burger$()\backslash$& place$\_$burger$\_$on$\_$table$()-$ for the chef

$-$ get$\_$burger$()\backslash$& go$\_$away$()-$ for the customer