# 7408：Good Treats

###### 题目描述
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.

###### 输入解释
Line 1: A single integer, N
Lines 2..N+1: Line i+1 contains the value of treat v(i)

###### 输出解释
Line 1: The maximum revenue Kousaka can achieve by selling the treats
###### 输入样例
5
1
3
1
5
2
###### 输出样例
43
###### 提示
Explanation of the sample:
Five treats. On the first day Kousaka can sell either treat #1 (value 1) or treat #5 (value 2).
Kousaka 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.

 时间上限 内存上限 1000 MS 128 MB