TRT  Treats for the Cows
FJ has purchased N (1 <= N <= 2000) 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..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 <= 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 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.
Input
Line 1: A single integer, N
Lines 2..N+1: Line i+1 contains the value of treat v(i)
Output
The maximum revenue FJ can achieve by selling the treats
Example
Input: 5 1 3 1 5 2 Output: 43
hide comments
Rishabh Joshi:
20150526 08:14:01
0.09 with top down dp.


Amit :
20150525 21:51:37
century :) :D 

Abhishek_2110:
20150525 07:19:31
both topdown and bottomup pass easily :) Last edit: 20151001 19:16:36 

Ankit:
20150329 16:27:33
Just a little common sense and it makes the DP seem difficult.


pol_djordje_24:
20150307 20:50:10
Please, i need help to understand the problem.


Ayur Jain:
20150202 18:41:07
Nice DP problem for beginners :) 

Jumpy:
20150120 18:40:48
It took so long to solve this problem. First I did Greedy  Failed. Then Recursive  TLE. After that DP  GOT AC with 0.00 sec and 18MB memory. 

Sampath Ravolaparthi:
20150116 16:25:38
OMG! I'm too Greedy!!!


Asheesh Pathak:
20150115 19:41:06
@Sampath Kumar Please tell me how you got AC. I'm having the same problem. 
Added by:  Nguyen Van Quang Huy 
Date:  20060215 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS PERL6 VB.NET 
Resource:  USACO FEB06 Gold Division 