FJ has purchased $N\ (1 \leq N \leq 2,000)$ yummy treats for the cows who get money for giving vast amounts of milk. FJ sells one treat per day and wants to maximize the money he receives over a given period time.
The treats are interesting for many reasons:

• The treats are numbered $1 \sim N$ and stored sequentially in single file in a long box that is open at both ends. On any day, FJ can retrieve one treat from either end of his stash of treats.
• Like fine wines and delicious cheeses, the treats improve with age and command greater prices.
• The treats are not uniform: some are better and have higher intrinsic value. Treat i has value $v_i\ (1 \leq v_i \leq 1,000)$.
• Cows pay more for treats that have aged longer: a cow will pay $v_i*a$ for a treat of age $a$.

Given the values $v_i$ of each of the treats lined up in order of the index $i$ in their box, what is the greatest value FJ can receive for them if he orders their sale optimally?

The first treat is sold on day $1$ and has age $a=1$. Each subsequent day increases the age by $1$.

Line 1: A single integer, $N$
Lines 2..N+1: Line $i+1$ contains the value of treat $v_i$

Line 1: The maximum revenue FJ can achieve by selling the treats

43

Five treats. On the first day FJ can sell either treat #1 (value 1) or treat #5 (value 2).
FJ sells the treats (values 1, 3, 1, 5, 2) in the following order of indices: 1, 5, 2, 3, 4, making 1x1 + 2x2 + 3x3 + 4x1 + 5x5 = 43.