Maximum Tracking Stack

Design and implement a specialized stack data structure that not only supports standard stack operations but also provides efficient access to and removal of the maximum element within the stack at any given time.

Your task is to create the MaximumTrackingStack class with the following methods:

• MaximumTrackingStack(): Initializes an empty stack object.
• void push(int x): Adds the integer element x onto the top of the stack.
• int pop(): Removes and returns the element currently at the top of the stack.
• int top(): Returns the element at the top of the stack without removing it.
• int peekMaximum(): Returns the maximum value present in the stack without removing it.
• int popMaximum(): Locates the maximum value in the stack, removes it, and returns it. If the stack contains multiple elements with the maximum value, only the topmost (most recently added) occurrence is removed.

Your implementation must achieve O(1) time complexity for the top operation and O(log n) time complexity for all other operations, where n is the number of elements in the stack.

This problem challenges you to combine multiple data structures to achieve efficient maximum tracking while maintaining the fundamental LIFO (Last-In-First-Out) behavior of a stack.