# Intersecting Rectangles

Consider, in a 2D space, a set of rectangles with edges that are parallel to the axis X and Y. One is the ma in rectangle and there are intersections between several rectangles. According to these intersections, one or more closed poly gons called “islands” can be defined. The main island is the one that contains the main rectangle. Figure 1 — The ten rectangles are defining 3 islands The proposed problem is to evaluate the area of the main island. For example, in Figure 1, consid- ering that polygon 1 is the main polygon, the main island is composed by polygons 1,2,3,5 and 10, so the problem here is to evaluate the area of the polygon presented in Figure 2. Figure 2 — The polygon defined by the main island Given a list of rectangles, starting with the main rectangle, the problem is to identify the main island and evaluate the correspondent area. Each rectangle is geometrically characterized by the coordinates of its bottom-left and upper-right corners; the maximum number of rectangles is 100; as a simplification, it can be considered that no coincidences between edges and vertices exist. Input The input begins with a single positive integer on a line by itself indicating the number of the cases following, each of them as described below. This line is followed by a blank line, and there is also a blank line between two consecutive inputs. The first line of the input contains the number of rectangles N (integer format) to be considered. Each one of the following N lines contains the coordinates of bottom-left and upper-right vertices of a rectangle, in the sequence xmin ymin xmax ymax, separated by a single space. The first recta ngle given is the main one.

2/2 Output For each test case, the output must follow the description below. The outputs of two consecutive cases will be separated by a blank line. One integer number that represents the main island area as defined above. Note: Figure 3 corresponds to the sample below. Input 1 9 2588 4 6 10 10 5 7 6 12 9 9 11 11 12 7 15 8 1336 4283 13 6 14 9 2 1 11 4 Sample Output 70 Figure 3 — Sample input