Fortress
In the year 2123, archaeologists uncovered the remains of an ancient fortress in the Leningrad Region. Unfortunately, some parts of the fortress have not survived. It is known that the fortress originally had six towers: three forming the vertices of a triangle, and the other three located at the midpoints of the triangle's sides. The precise positions of some towers are known, while others are not. Your task is to determine the positions of all the towers.
The illustration below depicts a possible top view of the fortress:
Input
The input consists of six lines, each describing a tower. If a tower's position is known, the line contains two integers separated by a space; if unknown, it contains two question marks ('?') separated by a space. The towers are listed in the order they are traversed, starting from an arbitrary corner tower.
Output
In the output, print IMPOSSIBLE if it is not feasible to uniquely determine the positions of all the towers. Otherwise, print POSSIBLE on the first line, followed by the positions of the towers on the next six lines, maintaining the same order as in the input. The coordinates should be printed with at least two decimal places.