Crane Balancing

Time limit1sMemory limit128 MB

Summary

Find the range of extra weight at the first vertex that keeps the polygon balanced on the x-axis.

Level: Medium6 of 10
Topics: Geometry, Math
Solved: No attempts yet

Problem

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.

Input

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

Output

Stable weight range, or unstable.

Examples5

Example 1

Input

Expected output

0 .. 1017

Example 2
Input
```
4
10 10
0 10
0 0
20 0
```
Expected output
```
0 .. inf
```
Example 3
Input
```
5
18 36
0 36
0 0
23 0
63 57
```
Expected output
```
138 .. inf
```
Example 4
Input
```
4
21 25
0 25
0 0
31 0
```
Expected output
```
0 .. inf
```
Example 5
Input
```
5
79 28
0 28
0 0
31 0
77 60
```
Expected output
```
57 .. 576
```