Is a point in a convex polygon? ------------------------------- Given a convex polygon and a point, is the point inside the polygon? The point is represented by its x- and y-coordinates and the polygon is represent by the number of points followed by the x- and y-coordinates of its points (in clockwise order). Input ----- The input begins with a single positive integer on a line by itself indicating the number of cases following, each of them on a line as described below. Each case is described by integers: x0 y0 n x1 y1 ... xn yn. (x0, y0) represents the point and (x1, y1),..., (xn, yn) represent the points of the polygon in clockwise order. Output ------ For each test case, the output is true if the point is within the polygon and false otherwise. Sample input ------------ 3 0 0 4 0 0 0 10 10 10 10 0 5 5 4 0 0 0 10 10 10 10 0 11 10 4 0 0 0 10 10 10 10 0 Sample output ------------- true true false