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$($n log n$).$

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$($n log n$).$ Show all your work. Hint: You can solve the recurrence relation in part $($b$),$ express it using Big$-$O$(),$ and justify as needed.