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 [MATH5] 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?

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.

见题面 Input 部分

见题面 Output 部分

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 $6$.