HMMT November 2022 U31

Given positive integers $a_{1}, a_{2}, \ldots, a_{2023}$ such that

$$a_{k}=\sum_{i=1}^{2023}\left|a_{k}-a_{i}\right|$$

for all $1 \leq k \leq 2023$, find the minimum possible value of $a_{1}+a_{2}+\cdots+a_{2023}$.