B"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, xe2 x80 x89q (p xe2 x80 x89 xe2 x89 xa0 xe2 x80 x89q) and q, xe2 x80 x89p are considered the same. Help Ksusha! Count the required expectation. The first line contains integer n (3 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89105) -- 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 xi, xe2 x80 x89yi (|xi|, xe2 x80 x89|yi| xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89106) -- 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 xe2 x80 x89- xe2 x80 x896."...