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
Lokesh: 2015-01-11 16:49:54

Top Down approach caused tle

KAI: 2015-01-01 16:32:32

easy DP, silly mistake costed wa's :)

ALISHA: 2014-12-19 19:13:05

its worth only with bottom up.
atleast it's 0.03 s faster in c++!! :D

eightnoteight: 2014-12-18 13:47:03

O(n) space and O(n*n) time complexity solution in python is giving tle,,
the time limit is too strict

agaurav77: 2014-12-14 12:04:19

If you are getting RE (SIGSEGV), try replacing int arr[N][N] and items[N] with arr[2001][2001] and items[2001]. AC finally!

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


Added by:Nguyen Van Quang Huy
Date:2006-02-15
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