KöMaL 2010 B4302

Soldiers are lined up along a line in the east-west direction, each of them facing north. The officer commands ``right turn''. Then they should all turn towards the east but, since they are at the very beginning of their military career, some of them get the order wrong and turn towards the west. Every soldier who now faces his neighbour concludes that they have made a mistake (disregarding the possibility of the neighbour making the mistake), and they make a 180-degree turn within 1 second. Then the process continues in the same way: every soldier who faces a neighbour makes a 180-degree turn within 1 second. Prove that the process will end in a finite number of steps.