Imagine that you work for a database company, which has a popular system for maintaining sorted sets. After a negative review in an influential technology website, the company has decided it needs to convert all of its indexing software from using sorted arrays to an indexing strategy based on using binary search trees, so as to be able to support insertions and deletions more efficiently. Your job is to write a program that can take a sorted array, A, of n elements, and construct a binary search tree, T, storing these same elements, so that doing a binary search for any element in T will run in O(log n) time. Describe an O(n)-time algorithm for doing this conversion.