Camila sells boxes in the shape of rectangular parallelepipeds, that is, the usual shape of a box.

If the height, width, and depth of a box are $$$a$$$, $$$b$$$, and $$$c$$$ respectively, Camila sells it for a price of $$$a^2+b^2+c^2$$$ pesos. The boxes are empty and are only made up of the surface. The material she uses costs half a peso (Argentine currency) per square unit. Therefore, manufacturing a box with height, width, and depth of $$$a$$$, $$$b$$$, and $$$c$$$ costs her $$$ab+bc+ca$$$ pesos.

Camila has a list of $$$N$$$ possible values for the height, width, or depth of the boxes. She only manufactures boxes such that each of its three dimensions belongs to this list of $$$N$$$ measurements she works with. There is no problem using the same value from the list for more than one of the three dimensions of a box.

If she chooses the dimensions $$$a,b,c$$$ of a box in such a way as to maximize her net profit (the difference between the selling price and the cost), how much can she earn at most from one sale?