MEMO 2016 I2

There are $n \ge 3$ positive integers written on a board. A move consists of choosing three numbers $a, b, c$ written from the board such that there exists a non-degenerate non-equilateral triangle with sides $a, b, c$ and replacing those numbers with $a + b - c, b + c - a$ and $c + a - b$ .

Prove that a sequence of moves cannot be infinite.