There are N computers in a computer club. It’s known which computers are to be connected with a cable in order to make the net work properly. It’s left to arrange the computers so that no two cables intersect and distance between every two computer would be greater than one. Regard the computers as points and the cables as line segments. The net is connected, i.e. every two computers are connected with some sequence of cables.
First line contains integer N (1 ≤ N ≤ 1000). Then N−1 lines follow. In each line there are two integers ai and bi, the numbers of computers that are to be connected with a cable (1 ≤ ai, bi ≤ N).
You should output N lines. In the ith line there should be two real numbers — coordinates of the ith computer. The absolute values of the coordinates shouldn’t exceed 1000.
Problem Author: Den Raskovalov (text by Aleksandr Bikbaev)
Problem Source: USU Junior Championship March'2005