You are given an unsorted array A$[1$ : n$]$ of n distinct positive integers. Design an algorithm that in O$($n $+$ M$)$ worst$-$case time, where M is the maximum possible integer within A finds the h$-$index of A$.$ The h$-$index is defined as the maximum integer h such that A$[1$ : n$]$ has at least h indices whose entry is at least h$.$ If instead of an O$($n $+$ M$)$ worst$-$case time algorithm, you design an algorithm with worst$-$case runtime of O$($n$),$ i$.$e$.,$ with no dependence on M$,$ you receive extra credit points.