Maximum Value?

Let $a_{1},a_{2},a_{3},\ldots,a_{n}$ be ‘n’ positive integers (not necessarily distinct) such that -

$a_{1}+a_{2}+a_{3}+\ldots+a_{n} = 16$

What is the maximum value of $a_{1}a_{2}a_{3}\ldots a_{n}$

Bonus - Generalise your findings for all positive integers.