Maximum Score

Chef is participating in a tournament. He must face $N$ opponents. If he wins against the $i$-th opponent, he will receive $A_i$ coins; whereas if he loses, he will receive $B_i$ coins. It's guaranteed that $A_i \ge B_i$. Chef doesn't want to bring too much attention to himself, so he decides that he will **lose at least once.** Under this constraint, what's the maximum total number of coin