Determine the largest constant $C>0$ satisfying the following property:

For any 2023-tuple $\left(a_{1}, a_{2}, \ldots, a_{2023}\right)$ of strictly positive real numbers that are pairwise distinct, the following inequality holds:

$$
\frac{a_{1}}{\left|a_{2}-a_{3}\right|}+\frac{a_{2}}{\left|a_{3}-a_{4}\right|}+\ldots+\frac{a_{2023}}{\left|a_{1}-a_{2}\right|}>C
$$