Let $x, y, z$ be positive real numbers such that $x + y + z = 1399$. Find the maximum value of $\lfloor x \rfloor y + \lfloor y \rfloor z + \lfloor z \rfloor x$, where $\lfloor a \rfloor$ is the greatest integer not exceeding $a$.

Let's think step by step and output the final answer within \boxed{}.
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