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
vonasj: 2016-08-13 21:20:40

Haskell Data.Array is too slow for that.

Mihir Saxena: 2016-07-10 07:14:59

50th!!

razor123: 2016-06-27 16:39:21

'age' is not a factor for memoizing as age is (i+n-j) where i and j are starting and end indices respectively.

baadshah_: 2016-06-26 21:40:45

AC in ONE GO!!!!!!!!!

adi_1996: 2016-06-25 14:00:11

try TWENDS after this :)

Tushar Singh: 2016-06-24 22:11:32

Reading comments helped me to get AC in one go!! :D

saurabh789: 2016-06-23 17:59:54

nice question my 50th!

sonali9696: 2016-06-22 21:01:44

My first thought was a 3D array for front,rear,age. But such large arrays can't be allocated.So think how age can be expressed in terms of front and rear and make 2D array for front,rear :) Happy coding!

saini428: 2016-06-13 03:06:54

simple recursion+memorization ,,,

Shivam Jha: 2016-06-01 12:46:21

a great tutorial for this by Michal Danilák .
https://www.quora.com/Are-there-any-good-resources-or-tutorials-for-dynamic-programming-besides-the-TopCoder-tutorial

Read the very first answer of this question.


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