Buffy and Willow are facing an evil demon named Stooge, living inside Willow's computer. In an effort to slow the Scooby Gang's compiting power to a crawl, the demon has replaced Willows hand-designed super-fast sorting routine with the following recursive sorting algorithm, known as StoogeSort. For simplicity, we think of Stoogesort as running on a list of distinct numbers. StoogeSort runs in three phases. In the first phase, the first 2/3 of the list is (recursively) sorted. In the second phase, the final 2/3 of the list is (recursively) sorted. Finally, in the third phase, the first 2/3 of the list is (recursively) sorted agairn. Willow notices some sluggishness in her system, but doesn't notice any errors from the sorting routine. This is because StoogeSort correctly sorts. For the first part of your problem, prove rigorously that StoogeSort correctly sorts. To keep things simple, you may assume in your proof that the length of the input is divisible by three. Your proof should use in Unfortunately, StoogeSort can be slow. Derive a recurrence describing its running time, and use the recurrence to bound the asymptotic running time of Stoogesort