On the unique factorisation of $R[x_1,y_1,...,x_n,y_n]/(x_1y_1+...+x_ny_n)$ where $R$ is UFD

Question

Let $R$ be a Noetherian UFD.

Then how to show that for every integer $n\ge 3$, the ring $A_n:= R[x_1,y_1,...,x_n,y_n]/(x_1y_1+...+x_ny_n)$ is a UFD ?

I'm not even sure how to show $A_n$ is an integral domain ...

Please help.