You are managing a company, and your employees are mostly working part$-$time,

on different shifts. For example, you may have someone working from $9$am to

$11$am$,$ another one working from $10$am to noon, and another one working from $1$pm to $4$pm$.$ Up to now, you trusted them to always be at work during the shifts

allocated to them, so you never really went to see them at work. However, you

heard rumors that you have one $($or more$)$ employee who manages to sign in for the work shift $($perhaps through a friend doing that for him$/$her$)$ but who is actually not physically there. You decide that for one day, you will go check a few times, to see if everybody is there as expected. However, because you are quite busy, you want to limit the number of times you will go there. Still, you need to make sure that you cover everyone during their shift. For the example above, you could go check at

$10$am$,$ and this would cover the first $2$ employees, and then you could go again at $2$pm to cover the last one $($it is not possible to check them all at once...twice is the smallest number of times you need here$).$ Note that you just want to check their

actual presence, not that they are truly there for their entire shift.

Give a greedy algorithm that would get as input the work time for each employee, and return a list of times that you would need to go check on them. You should

provide the following:

$-$ Formal proof that the algorithm always returns a correct answer, using a $$stay ahead$$ argument