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
shiva_hellgeek: 2013-05-27 19:52:56

An excellent problem on DP for begginers like me. :)

shashank: 2013-05-26 11:18:39

plz everyone join irc at #spoj

Sampath Kumar: 2013-05-22 05:36:08

give some tricky test cases.. getting WA , though i have tried many cases for which my algo is giving correct ans..

GOT AC..

Last edit: 2013-05-22 05:56:22
$!:D: 2013-05-16 04:48:16

Last edit: 2013-05-21 08:11:13
Ouditchya Sinha: 2013-04-26 08:25:44

Good DP problem, top down worked for me :)

mohit rathi: 2013-04-08 18:34:19

Simple DP..:D

Hani: 2013-03-07 15:20:47

somone provide more test cases.........???????

Akshaya Gupta: 2013-02-01 18:28:11

nice dp

innovolt: 2013-01-14 11:24:31

smone provide more test cases.........???????

gourav: 2012-12-24 20:17:27

nice problem.. but just do it if u r beginner.. still gave 3-4 WA :'(


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