I am trying to construct an example of a ring satisfying the followings.

A commutative noetherian ring with $1$ which is neither domain nor local and has a principal prime ideal of height $1.$

I know that a local noetherian ring having a height $1$ principal prime ideal is a domain. Actually I wanted to prove this without the local condition. I couldn't prove this hence I am looking for a counterexample. I need some help. Thanks.