$(20$ points$)$ Suppose that you can take $1,2,$ or $3$ steps at a time. Write a

recursive function to count the number of ways to climb a staircase of $n$

steps. For example, the function should return $4$ for $n=3$ because there

are four ways to climb a staircase of $3$ steps: $1)1,1,1,2)$

$2,1.$