## GUPTA MECHANICAL

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# [Solution] Swap and Take Codeforces Solution

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 ${a}_{1},{a}_{2},\dots ,{a}_{n}$ ($1\le {a}_{i}\le {10}^{6}$).

Output

Print a single integer — the maximum possible score.

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 $6$