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
scyth3r: 2015-07-10 19:16:02

no AC Python submission..... :<

Hunnybunch: 2015-06-01 20:43:54

Nice dp problem :)

Alaf Azam Khan: 2015-05-29 19:17:57

Nice Problem, tel laga k

Baymax: 2015-05-29 17:48:40

wa with faster i/o

anon: 2015-05-28 16:01:14

Can be done using both recursion and tabular form

Rishabh Joshi: 2015-05-26 08:14:01

0.09 with top down dp.
sweet!

Amit : 2015-05-25 21:51:37

century :) :D

Abhishek_2110: 2015-05-25 07:19:31

both top-down and bottom-up pass easily :)

Last edit: 2015-10-01 19:16:36
Ankit: 2015-03-29 16:27:33

Just a little common sense and it makes the DP seem difficult.
Great Question !!

pol_djordje_24: 2015-03-07 20:50:10

Please, i need help to understand the problem.
For example :
We have treats 1,3,1,5,2. If we sell treat that costs 1. Now threats costs 6,2,10,4. Now we sell threat that costs to and remaining threats costs 9,15 and 6. Using this method five times we get cost = 46.
What am i doing wrong?


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