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D. Ksusha and Square

time limit per test

4 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputKsusha 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}.

Examples

Input

3

0 0

5 5

5 0

Output

4.6666666667

Input

4

-1 3

4 5

6 2

3 -5

Output

8.1583333333

Input

3

17 136

859 937

16 641

Output

66811.3704155169

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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