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
kelaseek: 2014-07-17 11:40:55

the kinda array that i used was new to me

Vidur Katyal: 2014-07-16 18:55:58

Great DP question for beginners!! My 50th :D

Himanshu: 2014-07-01 20:07:11

HINT :: OBST Dynamic Programming

Chandan Singh: 2014-06-27 18:12:55

got it with memoization :)

sobriquet: 2014-06-22 20:32:10

Excellent DP
Simple recursion--TLE.
recursion+memoization--AC (0.84 s).
DP-bottom-top--AC (0.35 s).

Last edit: 2014-06-23 08:30:48
shade_1: 2014-06-18 21:21:58

finally my 1st DP...result AC

vicky: 2014-06-16 07:59:15

very easy dp AC in one go :)

fanatique: 2014-06-14 11:30:23

tricky test cases required...WA at 12th test case...

Last edit: 2014-06-14 11:46:03
SHIVAM DIXIT: 2014-04-23 15:59:47

finaly acc!!! after 5 wa...

AlcatraZ: 2014-03-22 09:09:15

Don't Go greedy :P
Input:
4
10 1 10 9
Output:
79


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