Extensions of flat modules and tensor products

Question

Let $R$ be a ring and let $$0 \rightarrow M_1 \rightarrow M_2 \rightarrow M_3 \rightarrow 0$$ be a short exact sequence of flat $R$-modules. Let $N$ be another $R$-module. Question: is the sequence $$0 \rightarrow M_1 \otimes_R N \rightarrow M_2 \otimes_R N \rightarrow M_3 \otimes_R N \rightarrow 0$$ necessarily exact? If we assumed that $N$ was flat and the $M_i$ were arbitrary, then this would be the definition of flatness, but I don't know about this other situation.