In the list of numbers $1, 2, \cdots, 9999$, the digits $0$ through $9$ are replaced with the letters $A$ through $J$, respectively. For example, the number $501$ is replaced by the string $FAB$ and $8243$ is replaced by the string $ICED$. The resulting list of $9999$ strings is sorted alphabetically. How many strings appear before $CHAI$ in this list?