According to the statement, any real point ~(x,y)~ is in Willson's territory if and only if ~|x-x_0| + |y-y_0| \le k~, where ~k~ is the maximum value of ~|x_i-x_0| + |y_i-y_0|~ for some ~i \in [1,N]~.

Note that this definition is real Manhattan distance. Note that all points in an axis-aligned square that is rotated 45-degree have the same Manhattan distance from the center of that square. Therefore, we simply compute the area of that square, where ~k~ is the Manhattan distance from ~(x_0,y_0)~ to one vertex of the square.

Note that even if Willson takes "infinitely small" horizontal and vertical steps, he is not walking diagonally, due to the laws of mathematics. Therefore, we should not use any form of Euclidean distance.

Time Complexity: ~\mathcal{O}(N)~