CF1736E Swap and Take

You're given an array consisting of $ n $ integers. You have to perform $ n $ turns. Initially your score is $ 0 $ . On the $ i $ -th turn, you are allowed to leave the array as it is or swap any one pair of $ 2 $ adjacent elements in the array and change exactly one of them to $ 0 $ (and leave the value of other element unchanged) after swapping. In either case(whether you swap or not), after this you add $ a_i $ to your score. What's the maximum possible score you can get?

The first line contains a single integer $ n $ ( $ 2 \le n \le 500 $ ). The second line contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 1 \le a_i \le 10^6 $ ).

Print a single integer — the maximum possible score.

In the first example, to get the maximum score we do as follows. Do nothing on the first turn, add $ 3 $ to the score. Swap the first and the second elements and turn $ 1 $ to $ 0 $ on the second turn, and add $ 3 $ to the score. The final score is $ 6 $ .