Maximizing by parts

Algebra Level 4

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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