[Grammar] would have gone...if I did not

[Oceanlike]

I don’t know how to write the sentence below correctly. It’s a mix of third conditional and second conditional which I know is incorrect.

I would have gone to the gathering if I did not have a prior appointment.

How should I write this sentence? I could not think of a way to change ‘did’ into the third condition.

Thank you! :-D

 

[Phaedrus]

I would have gone to the gathering if I had not had a prior appointment.
I would have gone to the gathering had I not had a prior appointment.