Automorphism of $\mathbb{A}^2$ which maps the finite set of points to the finite set of points

Question

Let $\mathrm{k}$ be infinite field. $P_1,\dots,P_n, Q_1,\dots,Q_n \in \mathbb{A}^2$ and $P_i \neq P_j, Q_i \neq Q_j$. I want to find automorphism(in a.g. sense) which maps $P_i$ to $Q_i$. I have tried use interpolation polynomials but with no benefits.. So i can construct morphism which maps $P_i$ to $Q_i$ but i don's sure that it's isomorphism.