Alist of n distinct integers a_1, a_2, a_n is called a mountain list if the elements reading from left to right first increase and then decrease. the location of the peak is the value i where a_i is greatest. for example, the list 1, 2, 3, 7, 6 is a mountain list with a peak at 4. we also consider a list of increasing numbers to be a mountain list with a peak at n, and a list of decreasing numbers to be a mountain list with a peak at 1. give pseudocode for an algorithm based on linear search that takes as input a mountain list a_1, a_2, a_n and returns the location of the peak. show that your algorithm does no more than n - 1 comparisons on any input of size n. give an algorithm based on binary search that takes as input a mountain list a_1, a_2, a_n and returns the location of the peak. your algorithm should be able to find the peak in any list of size 16 with no more than 4 comparisons (in general, up to k comparisons for a list of size 2^k.) you should provide pseudocode and an english description of your algorithm, but you do not need to prove that it meets the requirements for the number of comparisons.