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
demon: 2013-10-22 00:56:19

AC using DP.
Tried using a greedy approach..

(EDIT: Please do not post code.)

WA!! Why?? Any test cases?

Last edit: 2013-10-22 00:56:54
californiagurl: 2013-08-27 08:21:11

why am i getting sigsegv?
my array size <1000000

suryadev: 2013-08-09 15:32:01

if you get TLE in recursion then use memoization finally AC

$@WA!: 2013-07-26 21:40:40

for those who gets run time error exceed the array size...
for example.. v[2013]

Last edit: 2013-07-26 21:41:05
Deepanshu: 2013-07-11 17:56:50

i'm doing it using recursion but getting TLE

rishabhshinghal: 2013-07-04 18:11:08

nice question of DP:GOT AC at first

Aayush Gupta: 2013-07-04 10:10:54

i'm getting wrong answer after running...(12) anybody please suggest some test cases

achiever202: 2013-07-03 18:08:31

i am getting WA. anyone, any tricky cases ??

nagesh: 2013-06-18 15:21:33

nice :)


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