Percentiles and Box Plots · Superchallenge problem

Seven whole numbers from $0$ to $30$ have median $10$ and interquartile range $4$, and none of them is an outlier by the $1.5 \cdot \text{IQR}$ rule. ($Q_1$ and $Q_3$ are the medians of the lowest three and highest three values.) What is the difference between the largest and the smallest possible sum of the seven numbers?