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
Krzysztof Strojny: 2015-08-03 15:54:50

In Java be careful with input reading, scanner is too slow, use BufferedReader

Yuvak Patel: 2015-08-02 12:51:28

i m getting wrong answer at 7th case please help any body, i dont know what's wrong .Here's my solution http://ideone.com/oWxFGw

Anish Kumar: 2015-08-01 19:23:37

a good way to learn dp + memoization !

Last edit: 2015-08-01 19:23:51
just_code21: 2015-07-30 20:06:05

very nice question to learn bottoms up dp...in tabular form !!

jose torres torres: 2015-07-26 18:23:37

first DP =D AC

scyth3r: 2015-07-10 19:16:02

no AC Python submission..... :<

Hunnybunch: 2015-06-01 20:43:54

Nice dp problem :)

Alaf Azam Khan: 2015-05-29 19:17:57

Nice Problem, tel laga k

Baymax: 2015-05-29 17:48:40

wa with faster i/o

anon: 2015-05-28 16:01:14

Can be done using both recursion and tabular form


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