Middle European Mathematical Olympiad 2016 Problem I-2

There are $n \geq 3$ positive integers written on a blackboard. A move consists of choosing three numbers $a, b, c$ on the blackboard such that they are the sides of a non-degenerate non-equilateral triangle and replacing them by $a + b - c$, $b + c - a$ and $c + a - b$.

Show that an infinite sequence of moves cannot exist.