Let $A$ be a commutative ring. Let $N$ be a flat $A$-module. Let $S⊆A$ be a multiplicatively closed set. $S^{-1}N$ is flat $S^{-1}A$ module?

Question

Let $A$ be a commutative ring. Let $N$ be a flat $A$-module. Let $S⊆A$ be a multiplicatively closed set.

How can I prove $S^{-1}N$ is flat $S^{-1}A$ module ?

I see inverse argument ($S^{-1}N$ is flat implies $N$ is flat) in some texts, but I have never met the proof of this proposition. If this is an famous fact, reference(book, pdf,etc) is also appreciated. Thank you for your help.