ICPC 2014 · Problem C · Crane Balancing

Time Limit: 1 second

Wherever there is large-scale construction, you will find cranes that do the lifting. One hardly ever thinks about what marvelous examples of engineering cranes are: a structure of (relatively) little weight that can lift much heavier loads. But even the best-built cranes may have a limit on how much weight they can lift.

The Association of Crane Manufacturers (ACM) needs a program to compute the range of weights that a crane can lift. Since cranes are symmetric, ACM engineers have decided to consider only a cross section of each crane, which can be viewed as a polygon resting on the $x$-axis.

Figure C.1: Crane cross section

Figure C.1 shows a cross section of the crane in the first sample input. Assume that every $1\times 1$ unit of crane cross section weighs 1 kilogram and that the weight to be lifted will be attached at one of the polygon vertices (indicated by the arrow in Figure C.1). Write a program that determines the weight range for which the crane will not topple to the left or to the right.

Input

The input consists of a single test case. The test case starts with a single integer $n$ ($3 \le n \le 100$), the number of points of the polygon used to describe the crane’s shape. The following $n$ pairs of integers $x_{i}, y_{i}$ ($- 2 000 \le xi \le 2 000,0 \le yi \le 2 000$) are the coordinates of the polygon points in order. The weight is attached at the first polygon point and at least two polygon points are lying on the $x$-axis.

Output

Display the weight range (in kilograms) that can be attached to the crane without the crane toppling over. If the range is $[a, b]$, display $\lfloor a\rfloor$.. $\lceil b\rceil$. For example, if the range is $[1.5,13.3]$, display 1 .. 14. If the range is $[a,\infty )$, display $\lfloor a\rfloor$.. inf. If the crane cannot carry any weight, display unstable instead.

ACM-ICPC World Finals 2014 Problem C: Crane Balancing

Sample Input 1

7
50 50
0 50
0 0
30 0
30 30
40 40
50 40

Sample Output 1

0 .. 1017

Sample Input 2

7
50 50
0 50
0 0
10 0
10 30
20 40
50 40

Sample Output 2

unstable

ACM-ICPC World Finals 2014 Problem C: Crane Balancing