Laser Scan#4348
At point , there is a station equipped with a high-precision laser sensor, which performs line-of-sight scans. Its goal is to scan a moving robot, which travels along a straight path from point to point on the surface of the city. The laser beam travels along a straight line with infinite speed. There are skyscrapers in the city, modeled as rectangular parallelepipeds. The laser cannot pass through the interior of a skyscraper, but it can touch the surface of a skyscraper. The station will perform the scan at the earliest possible moment when the line of sight from to the robot is unobstructed.
Your task is to determine the coordinates where the robot will be when it is first scanned by the station.
The first line contains space-separated coordinates of : s_x, s_y, s_z (s_z \geq 0). The second line contains space-separated coordinates of points and : a_x, a_y, b_x, b_y. The robot moves on the ground plane, so its -coordinate is always zero. The third line contains an integer (0 \leq n \leq 100). Each of the following lines contains space-separated values l_x, l_y, r_x, r_y, (l_x < r_x; l_y < r_y; h > 0) — coordinates of the opposite corners of the base of each skyscraper and its height. The sides of the skyscrapers are parallel to the coordinate axes. All coordinates and heights are integers with an absolute value no greater than . No two skyscrapers share any point, point does not lie inside or on the border of any skyscraper, and segment does not intersect any of the skyscrapers.
If it is impossible for the station to ever scan the robot, output "Impossible". Otherwise, output the coordinates of the robot at the moment of scanning, with a precision of at least 10^{-7}.
Example 1