Swap and Take
Description
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.
Input
The first line contains a single integer $n$ ($2 \le n \le 500$).
The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^6$).
Output
Print a single integer — the maximum possible score.
2
3 1
5
7 3 9 6 12
6
52
Note
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 $6$.