Recall the matrix chain problem that we discussed in class. The input consists of n matricies A1, A2,..., An, and the problem computed the minimum number of operations required to multiply all n matricies. Note: the key issue is that the order in which the matricies were multiplied together changes the number of operations required. Also recall in class we derived a recurrence to count the number of ways to ascend n stairs if you take either 1 or 2 steps at a time. . . In this extra credit problem, you will derive a recurrence that counts the num- ber of different ways to multiply n matricies. For example, for 3 matricies, it is easy to see that there are only two ways: A (A2 A3) or (A1 A2) A3. Four matricies have 5 ways to choose from. Your answer should be in the form of a re- currence, and be accompanied by an explanation of why the recurrence captures the number of different ways to multiple n matricies. This problem will develop your skills at dissecting a problem into smaller versions of itself and combining them, except it will be aimed at counting, instead of developing an algorithm.