Problem 4 (20 points). The element distinctness (ED) problem is given a set S of n numbers, report "yes" if every element of S is unique and "no" if there are duplicates. Any comparison-based algorithm for this problem requires 12(n log n) time. Consider the closest-pair (CP) problem: Given a set R of n real numbers, which two numbers in R have the smallest difference? Show that any comparison-based algorithm for the closest-pair problem requires N2(n log n) time using the reduction method with the element distinctness lower bound