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 \( \approx 1.5304 \)