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Ex.3 (Cool Numbers) You are given distinct integers a1,,an. A pair of numbers (ai,aj) is called cool if ai=aj+5. - For the case where the n integers are unsorted, design an algorithm that runs in time (nlogn) and returns the total number of cool pairs as the output. Justify your answer. (Hint: start with a small example and count the "cool" pairs.) - A pair of numbers (ai,aj) is called super-cool if ai=aj+20. For the case where the n given integers are initially sorted, design an algorithm that runs in linear time (n) and returns the total number of "super-cool" pairs. Justify your