We want to design a divide and conquer algorithm that, given a list of n integer numbers, divides up the list into 3 (almost) equal-sized subparts, sorts each subpart recursively, and combines the solutions to form a sorted list of n integer numbers in ascending order. The algorithm's worst-case time complexity should be O(nlogn). a) Write an algorithm as a function only in C++/Java to solve the given problem. Pseudocode or English description is NOT accepted. b) Write the recurrence relation for the worst-case time complexity of your function at part (a). c) Justify why your function is upper-bounded by O(nlogn). Show all your work. Hint: You can solve the recurrence relation in part (b), express it using Big-O(), and justify as needed