Polygon Chain

A polygon $T$ is said to be *inside* a polygon $S$ if all points that lie strictly inside $T$ (not on the perimeter of $T$) also lie strictly inside $S$. A multiset of polygons $\{Q_1, Q_2, \ldots, Q_r\}$ is said to *form a chain* if there is a permutation $p_1, p_2, \ldots, p_r$ of the integers $1$ through $r$ such that for each $i$ ($1 \le i \lt r$), $Q_{p_i}$ is inside $Q_{p_{i+1}}$. You