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 × 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 ≤ n ≤ 100), the
number of points of the polygon used to describe the crane’s shape. The following n pairs of integers
xi , yi (−2 000 ≤ xi ≤ 2 000, 0 ≤ yi ≤ 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 bac .. dbe. For example, if the range is [1.5, 13.3], display 1 .. 14.
If the range is [a, ∞), display bac .. inf. If the crane cannot carry any weight, display unstable
instead.

Sample Input 1                               Sample Output 1
7                                            0 .. 1017
50 50
0 50
0 0
30 0
30 30
40 40
50 40

Sample Input 2                               Sample Output 2
7                                            unstable
50 50
0 50
0 0
10 0
10 30
20 40
50 40