What is the maximum number of elements that one can pick from the set of natural numbers from $1$ to $20$ such that the product of no two of them results in a perfect square or perfect cube?

$abcdefghij$ is a ten-digit number with distinct digits such that $a > b > c, d > e > f, g > h > i > j$. $a, b, c$ are consecutive even digits and $g, h, i, j$ are consecutive odd digits.If $d + e + f = 9$, then what is the value of $\left[\frac{a \times b \times c \times d}{i}\right]$ where [ ] denotes greatest integer function?