Kousaka has purchased N (1 <= N <= 2000) yummy treats for the cows who get money for giving vast amounts of milk. Kousaka sells one treat per day and wants to maximize the money she receives over a given period time.
The treats are interesting for many reasons:
• The treats are numbered 1..N and stored sequentially in single file in a long box that is open at both ends. On any day, Kousaka can retrieve one treat from either end of her 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 <= v(i) <= 1000).
• 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 Kousaka can receive for them if she 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.