Identify and protect the critical sections of the adder, multiplier and degrouper functions with a POSIX mutex. Try to keep your critical sections as small as possible.

Tip: man pthread_mutex_lock, pthread_mutex_unlock, pthread_mutex_init, ...

Check the return values of these functions for errors. Print a brief error message on stderr and exit your program with EXIT_FAILURE if one of them fails. Use the provided function printErrorAndExit().

Next, identify and protect the critical sections of the reader and sentinel functions, as well. Your code should now be immune to synchronization errors (e.g., race conditions, data corruption).