Let the deer into the city
We have already learned how to manage goats and gardens. Now, let's head a bit north and tackle the unique challenges of managing reindeer.
Reindeer herder Vanho has tied his reindeer, Ahtamak, to the fence of an oil platform, which is shaped like a convex polygon. The reindeer is secured with a long rope, allowing it to graze without wandering off. Around the oil platform, there is delicious lichen growing. Your task is to write a program that calculates the area outside the fence where the lichen is accessible to the reindeer. The shape of the fence, the tying point, and the length of the rope are provided in the input file.
Input
The first line of the input file contains an integer n - the number of vertices of the fence listed in clockwise order (3 ≤ n ≤ 100). The next n lines contain the coordinates of the fence's vertices in clockwise order. The following line contains three numbers: the coordinates of the point where the reindeer is tied to the fence and the length of the rope. All coordinates are integers and do not exceed 10^4 in absolute value. The numbers in each line are separated by spaces. It is guaranteed that the fence forms a strictly convex polygon and that the tying point of the reindeer lies on its boundary. Additionally, the length of the rope does not exceed half the perimeter of the fence.
Output
Output the area value with a precision of at least 10^{-3}.