You are given a unimodal array of n distinct elements, meaning that its entries are in increasing order up until its maximum element, after which its elements are in decreasing order. Give an algorithm to compute the maximum element of an unimodal array that runs in O$($logn$)$ time. Please provide $1)$ An intuitive explanation of the algorithm, $2)$ the pseudocode of your proposed solutions, $3)$ proof of correctness, and $4)$ an asymptotic analysis of the running time. $($Hint: A typical blueprint for solving a computational problem using only O$($log n$)$ opera$-$ tions is to perform a constant amount of work and then discard $\backslash$alpha n of the total input, for $0<\backslash$alpha $<1.)$