Percentiles and Box Plots · Superchallenge problem

Nine whole numbers have five-number summary $1, 4, 8, 12, 20$ (minimum, $Q_1$, median, $Q_3$, maximum; $Q_1$ and $Q_3$ are the medians of the lowest four and highest four values), and their mean is $9$. How many different data sets (lists in increasing order) are possible?