Chefs Homework Dilemma

Chef's school semester lasts for $n$ days. Chef's teacher gives the students some homework every day and it is compulsory to turn in the homework by the very next day. Chef knows that the number of minutes needed to complete the homework on the $i$-th day is $H_i$. Chef hates homework and wants to spend the minimum amount of time possible in doing homework. Luckily, he has a few tricks up his sle