Maximizing by parts

Algebra Level 5

Given that

27=i=1nai27=\displaystyle \sum_{i=1}^{n} a_i

Where each aia_i is a positive real number and nn is a positive integer.

Find the maximum value of

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

Input your answer as the first 3 digits of PP.

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