In this problem, you will design an algorithm to compute 2022n given nN as input. In each case, prove the correctness of your algorithm, and an upper bound on the number of multiplications used. 1. Using n1 many multiplications. 2. Using O(log2n) many multiplications, assuming n is a power of 2 , i.e., n=2k. 3. Using O(log2n) many multiplications for any n (not necessarily a power of 2 )