An array A[1..n is unimodal if it consists of an increasing sequence followed by a decreasing sequence, or more precisely, if there is an index such that mE 1,2, ...,n, such that for for all m iAli In particular, Alm] is the maximum element, and it is the unique "locally maximum" element surrounded by smaller element (Afm - 1andAfm + 1]). Give an algorithm to compute the maximum element of a unimodal input array AI1..n] in O(Ign) time. Prove the correctness of your algorithm, and prove the bound on its running time<.>