7. Assume that c> 0. Assume you had some kind of super-hardware that, when given two lists of length in that are sorted, merges them into one sorted list, and takes only n steps. (a) Write down a recursive algorithm that uses this hardware to sort lists of length n. (b) Write down a recurrence to describe the run time. (c) For what values of c does this algorithm perform substantially better than O(n log n)? Why is it highly implausible that this kind of super-hardware could exist for these values of c?