License plates in India begin with a code that identifies the state and district where the vehicle is registered, and this code is followed by a four$-$digit identification number.

These identification numbers are given sequentially, starting with $0000,0001,0002,$ etc. Once this sequence reaches $9999,$ a letter from the set $\{A,$dots,$Z\}$ is added $($in

order$),$ and once these run out, additional letters are added, and so on$.$ So the sequence of identification numbers proceeds as follows: $0000,0001,..,9999,40000,$

A$\mathrm{.}0001,...,$ A$9999,$ B$0000,$ B$0001,...,$ B$9999,...,$ Z$0000,$ Z$0001,...,$ Z$9999,$ A$\mathrm{.}40000,$ A$\mathrm{.}40001,....$

$($a$)$ How many identification numbers are there using two or fewer letters?