Consider the following problem: Given an array of integers, possibly with duplicates, we want to count the number of distinct integers contained in the array Write an algorithm (in pseudocode) which solves this problem USING A HASH TABLE. (Do NOT use sorting.) Your algorithm should use the hash table operations, Initialize, Insert, Retrieve and Member. Input to your algorithm is an array A and the size n of the array. The algorithm returns the number of distinct integers contained in the array. Assume your hash table has size at least 2n. Analyze the EXPECTED asymptotic running time of your algorithm on an array. Justify your running time analysis. Assume your hash table has size at least 2n. Analyze the WORST CASE running time of your algorithm on an array. Justify your running time analysis