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Problem Statement:

You are given a set of n types of rectangular 3-D boxes, where the i^th box has height h(i), width w(i) and length l(i) (all real numbers). You want to create a stack of boxes which is as tall as possible, but you can only stack a box on top of another box if the dimensions of the 2-D base of the lower box are each strictly larger than those of the 2-D base of the higher box. Of course, you can rotate a box so that any side functions as its base. It is also allowable to use multiple instances of the same type of box.

Solution:

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