Write a program that takes an integer n from the command line, generates a random permutation, prints the permutation, and prints the number of left-to-right minima in the permutation (the number of times an element is the smallest seen so far). Then write a program that takes integers m and n from the command line, generates m random permutations of length n, and prints the average number of left-to-right minima in the permutations generated. Extra credit: Formulate a hypothesis about the number of left-to-right minima in a permutation of length n, as a function of n.