Hibbard deletion degradation. Write a program that takes an integer N from the command line, builds a random BST of size N, then enters into a loop where it deletes a random key (using the code delete(select(Std Random .uniform(N)))) and then inserts a random key, iterating the loop N² times. After the loop, measure and print the average length of a path in the tree (the internal path length divided by N, plus 1). Run your program for N = 10², 10³, and 10⁴ to test the somewhat counterintuitive hypothesis that this process increases the average path length of the tree to be proportional to the square root of N. Run the same experiments for a delete() implementation that makes a random choice whether to use the predecessor or the successor node.