We want to use semaphores to implement a shared critical section $($CS$)$ among three threads T$1,$ T$2,$ and T$3.$ We want to enforce the execution in the CS in this order: First T$2$ must execute in the CS$.$ When it finishes, T$1$ will then be allowed to enter the CS; and when it finishes $T3$ will then be allowed to enter the CS; when $T3$ finishes then $T2$ will be allowed to enter the $CS,$ and so on$,($T$2,$ T$1,$ T$3,$ T$2,$ T$1,$ T$3,..)$

a$.$ What is the minimal number of semaphores we need in order to implement this ordering and mutual exclusion; and what are their initial values?

b$.$ Write the appropriate instructions and the $P()$ and $V()$ operations in the appropriate places in the pseudo$-$code below to fulfil th$.-$dered execution.

$\backslash$table$[[TI,T2,$T$3],[$While$($TRUE$),$While$($TRUE$),$While$($TRUE$)\{],[CS,CS,CS$