Let T_1 be the rooted tree consisting of a single root vertex. For n greaterthanorequalto 2, let T_n be the rooted tree consisting of a root vertex with four children, where the subtree rooted at each child is the tree T_n - 1. (a) Calculate how many paths in T_n start from the root vertex and end at a leaf vertex. (b) What is the minimum number of bits (0's and 1's) required to represent a path in T_n that starts at the root vertex and ends at a leaf vertex? Show your work and simplify your answer as much as possible. (c) Describe how to encode a path in T_n that starts at the root vertex and ends at a leaf vertex using the number of bits you gave in part (c). (d) Encode the bold path in T_3 using your method from part (c)