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
Ayur Jain: 2015-02-02 18:41:07

Nice DP problem for beginners :)

Jumpy: 2015-01-20 18:40:48

It took so long to solve this problem. First I did Greedy - Failed. Then Recursive - TLE. After that DP - GOT AC with 0.00 sec and 18MB memory.

Sampath Ravolaparthi: 2015-01-16 16:25:38

OMG! I'm too Greedy!!!
Don't know what to do....??
Will try again later.....;)

Asheesh Pathak: 2015-01-15 19:41:06

@Sampath Kumar Please tell me how you got AC. I'm having the same problem.

Lokesh: 2015-01-11 16:49:54

Top Down approach caused tle

KAI: 2015-01-01 16:32:32

easy DP, silly mistake costed wa's :)

ALISHA: 2014-12-19 19:13:05

its worth only with bottom up.
atleast it's 0.03 s faster in c++!! :D

eightnoteight: 2014-12-18 13:47:03

O(n) space and O(n*n) time complexity solution in python is giving tle,,
the time limit is too strict

agaurav77: 2014-12-14 12:04:19

If you are getting RE (SIGSEGV), try replacing int arr[N][N] and items[N] with arr[2001][2001] and items[2001]. AC finally!


Added by:Nguyen Van Quang Huy
Date:2006-02-15
Time limit:0.165s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: NODEJS PERL6 VB.NET
Resource:USACO FEB06 Gold Division