Gold has a face$-$centered cubic arrangement with a unit cell edge length of $4\mathrm{.}08.$ How many moles of gold fit in a gold nanoparticle sheet with a length of $83\mathrm{.}6nm,$ a width of $26\mathrm{.}1nm,$ and a thickness of $11\mathrm{.}2nm?$

Express your answer with the appropriate units.

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