Crane Balancing

A crane cross section is a polygon resting on the $x$-axis. Each $1 \times 1$ unit of area weighs 1 kg.

Extra weight is attached at the first polygon vertex. Find the range of attachable weight (in kg) for which the crane does not topple left or right. Print $\lfloor a \rfloor .. \lceil b \rceil$ for range $[a,b]$, or $\lfloor a \rfloor .. inf$ for $[a,\infty)$. Print unstable if no weight works.

• $n$ ($3 \le n \le 100$): number of vertices.
• Next $n$ lines: $x_i, y_i$. Weight attaches at the first vertex; at least two vertices have $y=0$.

Stable weight range, or unstable.