By using the Big Picard theorem show that $a$ is unique

By using the Big Picard theorem show that $a$ is unique

Let $f$ be a non polynomial analytic function in the whole complex plane.
Asume that the equation $f(s)=a$ has a finite number of solutions with
respect to $s$. Here $a‚0$. My question is: By using the Big Picard
theorem show that $a$ is unique.