# Maximizing by parts

Algebra Level 5

Given that

$27=\displaystyle \sum_{i=1}^{n} a_i$

Where each $a_i$ is a positive real number and $n$ is a positive integer.

Find the maximum value of

$P=\displaystyle \prod_{i=1}^n a_i$

Input your answer as the first 3 digits of $P$.

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