Suppose I have an algorithm that takes an array as input, does work proportional to n on the data, then splits the data into three groups. The size of each group depends on the exact input and can vary between [n/6] and [n/21. Then it recursively calls itself on each of the 3 groups. The base case is n 3 (the algorithm does 0(1) work in this case). Model the worst-case time complexity of this algorithm with a recurrence relation, then use a recursion tree to explain why the algorithm runs in 0(n log n) time.