B"You are working for the Gryzzl company, headquartered in Pawnee, Indiana. The new national park has been opened near Pawnee recently and you are to implement a geolocation system, so people won't get lost. The concept you developed is innovative and minimalistic. There will be n antennas located somewhere in the park. When someone would like to know their current location, their Gryzzl hologram phone will communicate with antennas and obtain distances from a user's current location to all antennas. Knowing those distances and antennas locations it should be easy to recover a user's location... Right? Well, almost. The only issue is that there is no way to distinguish antennas, so you don't know, which distance corresponds to each antenna. Your task is to find a user's location given as little as all antennas location and an unordered multiset of distances. The first line of input contains a single integer n ( 2 <= q n <= q 10^5 ) which is the number of antennas. The following n lines contain coordinates of antennas, i -th line contain two integers x_i and y_i ( 0 <= q x_i,y_i <= q 10^8 ). It is guaranteed that no two antennas coincide. The next line of input contains integer m ( 1 <= q n cdot m <= q 10^5 ), which is the number of queries to determine the location of the user. Following m lines contain n integers 0 <= q d_1 <= q d_2 <= q ... <= q d_n <= q 2 cdot 10^{16} each. These integers form a multiset of squared distances from unknown user's location (x;y) to antennas. For all test cases except the examples it is guaranteed that all user's locations (x;y) were chosen uniformly at random, independently from each other among all possible integer locations having 0 <= q x, y <= q 10^8 . For each query output k , the number of possible a user's locations matching the given input and then output the list of these locations in lexicographic order. It is guarantee"...