Suppose proc$1$ and proc$2$ run in two separate threads and that each procedure is called in its respective thread exactly once. Variables x and a are global and shared between threads and x is initialized to $0.$ Further, assume the increment and decrement operations are atomic. The calls to proc$3$ in proc$1$ and proc$2$ should be replaced with calls to proc$3$a and proc$3$b depending on the part of the question. a$)$ If proc$1$ and proc$2$ call proc$3$a in lines $10$ and $18,$ is the final value of global variable x guaranteed to be $0?$ Justify your answer. b$)$ What if proc$1$ and proc$2$ call proc$3$b$?$ Justify your answer. c$)$ With proc$1$ and proc$2$ still calling proc$3$b$,$ modify proc$1$ and proc$2$ with condition variable go to guarantee the final value of x is $2.$ Specifically, give the lines where pthread$\_$cond$\_$wait and pthread$\_$cond$\_$signal should be inserted into the code listing. Justify your answer briefly. Make the assumption that proc$1$ acquires lock$\_$a before proc$2.$ Also recall that pthread$\_$cond$\_$wait$($&go$,$ &lock$\_$a$)$; will temporarily release lock$\_$a and block the calling thread until pthread$\_$cond$\_$signal$($&go$)$; is called in another thread, at which point the waiting thread will be unblocked and reacquire lock$\_$a$.$