The cohomology of meromorphic functions

Question

Let $A$ be a sheaf such that $$A(U) = \{ f \in \mathbb M(U): f \in \mathbb{O}(U \backslash\{p_1,\ldots, p_n\}) \ \mbox{with at worst a simple pole at}\ p_i \}. $$, where $\mathbb M(U)$ means the set of meromorphic functions on $U$ and $\mathbb O(U)$ means the set of holomorphic functions on $U$. What is the cohomology of $A$ on the Riemann sphere?