In the programming language Python, variable names use the alphabet $\{A,B,$dots,$Z,a,b,$dots,$z,0,1,$dots,$9,{?}_{-}\}$ of size $63.$ Variable names cannot start with a number $($but $\_$ is allowed$).$

$($a$)$ How many variable names are there of length $3?$

$($b$)$ What is the smallest integer $n$ such that there are at least $1$ billion variable names of length $n?$