$(3\mathrm{.}1\mathrm{.}4)$ An algorithm is said to be tail recursive when all of its recursive calls are in $$tail position$$: when each recursive call is the final operation that the algorithm must perform before returning. Such algorithms can often be more aggressively optimized into more efficient machine code. Consider the following recursive algorithm: MaxDifference$($A $=($a$0$ a$1$ an $1))$ Input: A finite sequence A of n $2$ integers Output: The largest difference between consecutive integers in A $1$: if n $=2$ then $2$: return a$0$ a$13$: else $4$: return max a$0$ a$1$ MaxDifference$(($a$1$ a$2$ an $1))$ This algorithm finds the largest difference between consecutive elements in a sequence. For example, given A $=(82951),$ it returns $29=7.$ However, it is not tail recursive, because it must perform the max a$0$ a$1$ operations after its recursive call. Rewrite this algorithm tail recursively $($and also non$-$generatively$).$