Suppose we are given a set of rectangular 3-D objects, where the ith object has width w(i), depth d(i), height h(i) (all real numbers). We want to create a stack of objects which is as tall as possible, trying to maximize the total height, but we can only stack an object on top of another object if the dimensions of the 2-D base of the lower object are each larger than or equal to those of the 2-D base of the higher object. This rule applies to any object that you put on the first object. Design an algorithm with the dynamic programming approach to solve the problem described above and apply your algorithm to the set of objects below: S= {(20,40,10), (40, 70, 100), (50,70,20),(60,60,30), (10,40,30), (20,20, 120), (10,50, 100), (30,30,20)}

where each tuple represents (width, depth, height) of an object respectively.