E. Swap and Take
time limit per test
2 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

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?

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.

Examples
Input
2
3 1
Output
6
Input
5
7 3 9 6 12
Output
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 $$$6$$$.