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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.
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.
Display the weight range (in kilograms) that can be attached to the crane without the crane toppling over. If the range is \(\left[ a,b \right]\) , display \(\left\lfloor a \right\rfloor ..\left\lceil b \right\rceil \). For example, if the range is \(\left[1.5, 13.3 \right]\), display
1 .. 14. If the range is \(\left[ a, \infty \right ) \) , display \(\left\lfloor a \right\rfloor .. inf\). If the crane cannot carry any weight, display
7 50 50 0 50 0 0 30 0 30 30 40 40 50 40
0 .. 1017