How were the ranks of ancient doctors divided?

Ancient documents put doctors and fortune tellers, innkeepers and bakers at the same level, and these people are at most the middle class of society. However, a few doctors, with their superb medical skills, squeezed into the court and served as court doctors, thus gaining a higher social status. These doctors specialize in serving kings, queens and dignitaries. Sometimes, they are sent to foreign countries to entertain foreign heads of state, expand their prestige as messengers of peace and consolidate friendly relations between allies.