In the interaction between a hammer and the nail it hits, is a force exerted on the nail? on the hammer? how many forces occur in this interaction?

When you hit a hammer on the head of a nail, all the momentum associated with hammer is transferred into nail. And due to this, the surface of nail gets deformed or if you touch it you can feel the rise in temperature. When you hit a hammer on nail, hammer exerts force on nail and by Newton's 3rd law, nail will also exert a force on the hammer perpendicular to the surface of the hammer of same magnitude but its direction will be reversed. Thus, only 2 forces acts in this interaction and they are action-reaction pairs.