KöMaL 2018 B4955

Let $n$ be a positive integer. What is the largest possible number of ordered triples of non-negative integers $(x_1,y_1,z_1),(x_2,y_2,z_2),\ldots$ such that the following conditions hold: (1) For all $i$, $x_i + y_i + z_i = n$. (2) The numbers $x_1,x_2,\ldots$ are all different, the numbers $y_1,y_2,\ldots$ are all different, and the numbers $z_1,z_2,\ldots$ are also all different. Give an example for such a sequence of maximum length with the required property.