George plays the following game: At every step he can replace a triple of integers $(x,y,z)$ which is written on the blackboard, with any of the following triples: (i) $(x,z,y)$ (ii) $(-x,y,z)$ (iii) $(x+y,y,2x+y+z)$ (iv) $(x-y,y,y+z-2x)$ Initially, the triple $(1,1,1)$ is written on the blackboard. Determine whether George can, with a sequence of allowed steps, end up at the triple $(2021,2019,2023)$, fully justifying your answer.