Задача Gunman

Описание

Consider a 3D scene with OXYZ coordinate system. Axis OX points to the right, axis OY points up, and axis OZ points away from you. There is a number of rectangular windows on the scene. The plane of each window is parallel to OXY , its sides are parallel to OX and OY . All windows are situated at different depths on the scene (different coordinates z > 0).

A gunman with a rifle moves along OX axis (y = 0 and z = 0). He can shoot a bullet in a straight line. His goal is to shoot a single bullet through all the windows. Just touching a window edge is enough.

Your task is to determine how to make such shot.

Формат входных данных

The first line of the input file contains a single integer number n (2 ≤ n ≤ 100) — the number of windows on the scene. The following n lines describe the windows. Each line contains five integer numbers x1 _i , y1 _i , x2 _i , y2 _i , z _i (0 < x1 _i , y1 _i , x2 _i , y2 _i , z _i < 1000). Here (x1 _i , y1 _i , z _i ) are coordinates of the bottom left corner of the window, and (x2 _i , y2 _i , z _i ) are coordinates of the top right corner of the window (x1 _i < x2 _i , y1 _i < y2 _i ). Windows are ordered by z coordinate (z _i > z _i-1 for 2 ≤ i ≤ n).

Формат выходных данных

Output a single word “UNSOLVABLE” if the gunman cannot reach the goal of shooting a bullet through all the windows.

Otherwise, on the first line output a word “SOLUTION”. On the next line output x coordinate of the point from which the gunman must fire a bullet. On the following n lines output x, y, z coordinates of the points where the bullet goes through the consecutive windows. All coordinates in the output file must be printed with six digits after decimal point.