Consider a set of positive integers X = {$1, . . . ,In} where each 1',- is represented in base 2' that is, over the alphabet {DUES - 1} and I,- E \"a\" for some constant c. We assume for simplicity that s divides clog 11. Suppose we store all 1',- strings in a compressed trie T in the following way. For each node v E T, we maintain an arrayr A\" of size 2". In this array, A\" [1'] contains a pointer to the child 11;,- of 1: such that the edge of T connecting 1: and 113- is labelled with the symbol 3' If no such 1:]- exists, then At. [3'] = 13'. [a] What is the upper bound on the maximum height of T in terms of s, n, and c? [b] 'What is the upper bound on the maximmn space usage of all arrays Au? Consequently, what is the upper bound on the maximum space usage of T? {c} 1'.|"1.u"hat time is needed to search for a key It in T