Archangel of the Science is reporting:
“O, Lord! Those physicists on the Earth have discovered a new elementary particle!”
“No problem, we’ll add another parameter to the General Equation of the Universe.”
As physics develops and moves on, scientists find more and more strange elementary particles, whose properties are more than unknown. You may have heard about muons, gluons and other strange particles. Recently scientists have found new elementary particles called troubleduons. These particles are called this way because scientists can create or annihilate them only in couples. Besides, troubleduons cause trouble to scientists, and that’s why the latter want to get rid of them. You should help scientists get rid of troubleduons.
Experimental set consists of eight cameras, situated in the vertices of a cube. Cameras are named as A, B, C, …, H. It is possible to generate or annihilate two troubleduons in neighbouring cameras. You should automate the process of removing troubleduons.
The only line contain eight integers ranging from 0 to 100, representing number of troubleduons in each camera of experimental set.
Output sequence of actions leading to annihilating all troubleduons or “IMPOSSIBLE”, if you cannot do it. Actions should be described one after another, each in a separate line, in the following way: name of the first camera, name of the second camera (it should be a neighborough to the first one), “+” if you create troubleduons, “-” if you destroy them. Number of actions in the sequence should not exceed 1000.
1 0 1 0 3 1 0 0
0 1 0 1 2 3 2 2
Problem Source: Ural Collegiate Programming Contest, April 2001, Perm, English Round