OSN 2018 Problem 5

Find all triples of reals $(x,y,z)$ satisfying: $$\begin{cases} \frac{1}{3} \min \{x,y\} + \frac{2}{3} \max \{x,y\} = 2017 \frac{1}{3} \min \{y,z\} + \frac{2}{3} \max \{y,z\} = 2018 \frac{1}{3} \min \{z,x\} + \frac{2}{3} \max \{z,x\} = 2019 \end{cases}$$