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
AC: 2014-10-19 13:20:07

Last edit: 2014-10-19 16:04:44
Sba Baranwal: 2014-10-18 10:48:03

whats wrong with 12th case???
can some one provide more test cases....

jack sparrow: 2014-10-15 19:48:22

first make recusion solution and then use memoization :D

അഭി : 2014-10-12 11:52:04

Try to do in O(N) space.

Last edit: 2014-10-12 12:43:45
Rajat (1307086): 2014-10-08 16:24:29

Can't believe I solved it without any help. ....

Diptesh Patel: 2014-09-29 09:47:28

what is wrong with case:12 ? :(

Kishlay Raj: 2014-09-22 14:27:12

my 50th cakewalk :P

Deepanker Aggarwal: 2014-09-20 16:50:58

50th :)...Btw any clues on how can this be done iteratively?

Arun Karthikeyan: 2014-09-13 19:54:33

Java Recursion TLE, same soln AC in C++
Java Iteration DP AC.


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