Ksusha and Square
Ksusha is a vigorous mathematician. She is keen on absolutely incredible mathematical riddles. 

Today Ksusha came across a convex polygon of non-zero area. She is now wondering: if she chooses a pair of distinct points uniformly among all integer points (points with integer coordinates) inside or on the border of the polygon and then draws a square with two opposite vertices lying in the chosen points, what will the expectation of this square's area be?

A pair of distinct points is chosen uniformly among all pairs of distinct points, located inside or on the border of the polygon. Pairs of points *p*,<=*q* (*p*<=≠<=*q*) and *q*,<=*p* are considered the same.

Help Ksusha! Count the required expectation.
The first line contains integer *n* (3<=≤<=*n*<=≤<=105) — the number of vertices of Ksusha's convex polygon. Next *n* lines contain the coordinates of the polygon vertices in clockwise or counterclockwise order. The *i*-th line contains integers *x**i*,<=*y**i* (|*x**i*|,<=|*y**i*|<=≤<=106) — the coordinates of the vertex that goes *i*-th in that order.
Print a single real number — the required expected area. 

The answer will be considered correct if its absolute and relative error doesn't exceed 10<=-<=6.
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