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
dennislo: 2018-06-27 18:59:16

Think about the recursive approach first.

shivhek25: 2018-06-27 10:45:55

Last edit: 2018-06-27 15:34:22
kkislay20: 2018-06-08 04:59:22

A very very nice problem....variation of matrix chain multiplication but this time i did it totally by myselef.

aakash2509: 2018-06-05 14:21:19

Nothing is wrong with the test case 12 . Just make sure that you are using the storage array within bounds [2001][2001] .

Last edit: 2018-06-06 09:23:51
hai_dee: 2018-03-10 10:06:18

Don't even bother trying to do it in Python. I did it in Python using what I'm sure was an optimal algorithm and TLE'ed. Eventually decided to convert my algorithm to C++ despite not having used that language for 10 years. Result was 0.00 second AC.

sherlock11: 2018-02-03 11:57:42

similar problem TWENDS.

ameyanator: 2018-01-13 18:55:32

used a std::map<pair<int,int>,int> got tle. Got AC with 2D array memoization

subhag0721: 2017-09-05 10:45:02

map + pair => TLE,
2-d array => AC

shauryauppal: 2017-06-14 22:46:22

I first did with greedy approach not attentive.
Got WA
thought of tc->
4
6 1 5 5

then did this with memoization in attempt two and got success

Last edit: 2017-06-14 22:46:49
satyabrat35: 2017-06-13 20:38:18

simple DP try TWENDS.... :)

Last edit: 2017-06-13 20:39:14

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