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.

Input

The first line contains integer $*n*$ $(3 ≤ *n* ≤ 10^{5})$ — 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 $*x*_{*i*}, *y*_{*i*}$ $(|*x*_{*i*}|, |*y*_{*i*}| ≤ 10^{6})$ — the coordinates of the vertex that goes $*i*$-th in that order.

Output

Print a single real number — the required expected area.

The answer will be considered correct if its absolute and relative error doesn't exceed $10^{ - 6}$.