An AugmentedStack s is an ADT that maintains any generic stack with comparable element type under the following operations, each requiring O(1) worst-case time: s.push(x): Insert element x on top of s. s.pop(): Remove and return the top element of s (if not empty). Return null if s is empty. s.getMin(): Return the minimum element on s (if not empty). Return null if s is empty. (Upon return from this method, s should be in the same state as it was before this method was called. In particular, the minimum element is not removed from s.) Also include the usual operations s.isEmpty() and s.top() with the same meaning as for conventional stacks that run in O(1) worst-case time. Design and analyze a data structure that implements this ADT with the specified running times. Hint: maintain additional private auxiliary fields in your augmented structure.