SOLVE
LATER
You are given a Simple Polygon $$P$$ in $$XY$$ plane with $$n$$ vertices, given in clockwise OR anticlockwise order, and a point $$p$$ in the same plane.
All the vertices of $$P$$ and point $$p$$ have integer coordinates.
A point $$q$$ is chosen uniformly randomly inside the polygon. Find the expected euclidean distance of $$q$$ from $$p$$
Input
The first line contains $$n$$, the number of vertices of polygon $$P$$.
The next line contains two integers $$(x_0,y_0)$$, the coordinates of point $$p$$
$$i^{\text{th}}$$ of the next $$n$$ lines contains two integers $$(x_i,y_i)$$, the coordinates of $$i^{\text{th}}$$ vertex of polygon.
Output
Print only one line containing the expected distance of a point randomly chosen inside $$P$$ from $$p$$, rounded to the nearest integer.
Constraints
$$ n \le 10^5 $$
$$ 0 \le x_i,y_i \le 10^6$$, for all $$0 \le i \le n$$
All points in the input are distinct.
The expected distance of center of a square of length $$4$$ from a point chosen randomly inside it is $$ \approx 1.5304 $$