Consider the earliest$-$finish$-$time$-$first greedy strategy for the interval partitioning algorithm shown below, and prove or disprove if this strategy is optimal. In the algorithm, a lecture j is compatible with a classroom if its time interval $($sj$,$ fj$)$ does not overlap the time interval of any other job already scheduled in the classroom. Hint: remember we used a structural bound called $$depth$,$ which denotes the largest number of intervals overlapping at any time.