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
Dhruv Mullick: 2014-12-06 19:21:48

Going Top Down destroys the fun. Try using Bottom up approach :)

Last edit: 2014-12-06 19:22:02
Vaibhav Gosain: 2014-12-03 15:23:27

do TWENDS if u are having a problem with this one :)

Prashant Jha: 2014-11-05 23:52:22

Nothing wrong with case 12. Your solution might have failed a previous test case and was still judged for 12 test cases. Refer to the quora link (mimino) in one of the comments. Explains it beautifully. Also, top down solution is about 1 seconds slower than bottom up DP, but still passes the time limits, of course.

alhussein: 2014-10-31 14:38:10

what is wrong with case:12 ? :(

Ankit Aggarwal : 2014-10-22 16:36:52

http://www.quora.com/Are-there-any-good-resources-or-tutorials-for-dynamic-programming-besides-the-TopCoder-tutorial/answer/Michal-Danil%C3%A1k

AC: 2014-10-19 13:20:07

Last edit: 2014-10-19 16:04:44
Sba Baranwal: 2014-10-18 10:48:03

whats wrong with 12th case???
can some one provide more test cases....

jack sparrow: 2014-10-15 19:48:22

first make recusion solution and then use memoization :D

അഭി : 2014-10-12 11:52:04

Try to do in O(N) space.

Last edit: 2014-10-12 12:43:45
Rajat (1307086): 2014-10-08 16:24:29

Can't believe I solved it without any help. ....


Added by:Nguyen Van Quang Huy
Date:2006-02-15
Time limit:0.165s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: NODEJS PERL6 VB.NET
Resource:USACO FEB06 Gold Division