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
Afrizal: 2014-03-01 07:27:30

i use top-down recursion and still got AC

nitesh kumar: 2014-02-04 14:47:47

cakewalk!!!!!!

Akash Singh: 2014-02-03 09:39:20

in JAVA
DP + I/O optimization= AC..
only DP=TLE.

Pritam Prakash: 2014-01-30 22:43:01

easy 2D DP problem.
Apply bottom-up approach.

Last edit: 2014-01-30 22:52:33
Vipul Pandey: 2014-01-30 22:41:57

very nice dp for beginners. Enjoyed solving it.

Last edit: 2014-01-30 22:46:23
Jitesh: 2014-01-04 09:28:55

Loved solving it. Nice dp. :)

Siddharth: 2013-12-03 09:52:33

Memoized recursion gives TLE in java but AC in C

californiagurl: 2013-11-17 05:20:14

@Nguyen Van Quang Huy-WA on 12th test case... plz help out. using bottom-up approach.

edit : plz visit the following link
http://www.spoj.com/forum/viewtopic.php?f=3&t=13297&sid=97211a4c3bf232645cfb357d0716a9e2
i dont get the reason for wrong answer

Last edit: 2013-11-21 06:59:30
jkelava6: 2013-11-12 20:28:46

We've beeing working DP last time and teacher gave us this = DP! Recursive approach is slow, do iterative, but be carefull at greedy approach, and WA comes for example at 6 1 1 1 5 5! Interesting, it needs improvment...

Last edit: 2013-11-12 20:29:12
Ouditchya Sinha: 2013-09-21 09:34:20

@Tushar Poddar : Check this http://ideone.com/3hShKy ,correct answer should be 10535, while your code is giving garbage output. Greedy approach will always fail for cases such as the one I gave( think why ). Also don't post your code here, use the forum. Kindly remove your code. :)


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