Let $X\sim$Hyp($N,l,n$) and $h:\{0,1,...,\min(l,n)\}\to\mathbb{R}$. Prove that there is no unbiased estimator $h(X)$ for the unknown parameter $N$.

Question

Let $X$ be hypergeometrically distributed with the parameters Hyp(N,l,n). Of those parameters, $N$ is unknown. I have got to argue (preferably prove) that there doesn't exist an unbiased estimator $\hat{N}:=h(X)$ where $h:\{0,1,\dots,\min(l,n)\}\to \mathbb{R}$.

My issue is I don't know how to calculate the expected value of $\hat N$ as I don't know the probability distribution of $h(X)$. My other idea was to try something with the Jensen inequality when it becomes an equality so that I could calculate the expected value of $X$ before applying $h$ to it. However, this would only cover a fraction of the possible functions for $h$ and leaves me more uncertain about this assertion being true than ever (and I know it is or else it wouldn't be printed in my textbook).

Any help would be greatly appreciated.