PUMaC 2011 Algebra B Problem 6

Shirley has a magical machine. If she inputs a positive even integer n, the machine will output n / 2, but if she inputs a positive odd integer m, the machine will output m+3. The machine keeps going by automatically using its output as a new input, stopping immediately before it obtains a number already processed. Shirley wants to create the longest possible output sequence possible with initial input at most 100. What number should she input?