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.