Largest minus smallest number with digit product 96

Let $A$ be the set of positive integers whose decimal digits have product $96$, where no digit may equal $1$ (so $A$ is finite). If $x=\min A$ and $y=\max A$, find $y-x$.

321954. Since $96=2^5\cdot3$, the longest such number uses digits $3,2,2,2,2,2$, so $y=322222$. The fewest digits possible is three (no two digits multiply to $96$), and the three-digit options are $\{2,6,8\},\{3,4,8\},\{4,4,6\}$; the smallest is $x=268$. So $y-x=321954$.