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 ≤ 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.

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.

Ksusha and Square

Examples