Chef and Patients

Dr. Chef is treating COVID-19 patients. There is a queue of $N$ patients (numbered from patient $1$ at the front of the queue to patient $N$ at the back) outside his clinic. You, his assistant, found out that for each valid $i$, the $i$-th patient has an *illness level* $A_i$. Chef treats patients based on their health, i.e. a patient with a higher illness level is always treated before any patie