2. (6 points) The hard way perform a recursion tree analysis to get the asymptotic running time of mergesort3. (a) Draw a picture of the recursion tree for n=27 (sorting 27 items). (b) How many sub-problems are there at any given level (use Lin your equation)? Here, sub- problems refers to a call to the merges function. Notel: the root is Level O, the second level is Level 1, and leaves are at Level logs(n). (c) How many elements are there for a given sub-problem (call to merge3) found in level L? (d) How much work is performed at a given level L? This equation will be based on your answers to parts (b) and (c). (e) What is the total computational cost of mergesort3? (f) What is the asymptotic complexity of mergesort3