2. Write a program that efficiently computes the number of strings of length n over {A, B, C} that have at least one occurrence of BAB and no occurrence of ACA. Your program should compute the values exactly for n up to 200 and run in less than 10 seconds. Run your program for n = 91 and include a screen shot the source code as well as the output. (Your code should also copied and pasted to the PDF document submitted.) Test case: The number of such strings for n = 27 is 2039428171297.