B"Mainak has a convex polygon mathcal P with n vertices labelled as A_1, A_2, ldots, A_n in a counter-clockwise fashion. The coordinates of the i -th point A_i are given by (x_i, y_i) , where x_i and y_i are both integers. Further, it is known that the interior angle at A_i is either a right angle or a proper obtuse angle. Formally it is known that: Mainak's friend insisted that all points Q such that there exists a chord of the polygon mathcal P passing through Q with length not exceeding 1 , must be coloured color{red}{ text{red}} . Mainak wants you to find the area of the coloured region formed by the color{red}{ text{red}} points. Formally, determine the area of the region mathcal S = {Q in mathcal{P} | Q text{ is coloured } color{red}{ text{red}} } . Recall that a chord of a polygon is a line segment between two points lying on the boundary (i.e. vertices or points on edges) of the polygon. The first line contains an integer n ( 4 <= n <= 5000 ) -- the number of vertices of a polygon mathcal P . The i -th line of the next n lines contain two integers x_i and y_i ( -10^9 <= x_i, y_i <= 10^9 ) -- the coordinates of A_i . Additional constraint on the input: The vertices form a convex polygon and are listed in counter-clockwise order. It is also guaranteed that all interior angles are in the range [90^ circ ; 180^ circ ) . Print the area of the region coloured in color{red}{ text{red}} . Your answer is considered correct if its absolute or relative error does not exceed 10^{-4} . Formally, let your answer be a , and the jury's answer be b . Your answer is accepted if and only if frac{|a - b|}{ max{(1, |b|)}} <= 10^{-4} . In the first example, the polygon mathcal P can be visualised on the Cartesian Plane as: "...