We consider a multi$-$threaded process $($with $80$ threads$)$ with multiple phases. Whenever a thread finishes a phase, it will call check$()$: If fewer than $\backslash (3/4\backslash )$ of all threads are in sleep it will be put into sleep as well, otherwise it will wake up all of the sleeping thread and they will together proceed to the next phase. Implement check$()$ with help of mutex and condition variable, the pseudo syntax of which is defined here:

$```$

mutex m; cond c;

mutex$\_$init$($m$,$ NULL$)$; cond$\_$init$($c$,$ NULL$)$;

mutex$\_$lock$($m$)$; mutex$\_$unlock$($m$)$; cond$\_$wait$($c$,$m$)$; cond$\_$signal$($c$)$; cond$\_$broadcast$($c$)$;

$```$

Use the following code framework.

$```$

mutex m;

cond c;

mutex$\_$init$($m$,$ NULL$)$;

cond$\_$init$($c$,$ NULL$)$;

$/*$ P$$t any additional variables and$/$or their initial values below $*/$

$```$

$/*$ It is called whenever a thread finishes a phase $*/$

void check$()\backslash \{$