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
Tushar Singh: 2016-06-24 22:11:32

Reading comments helped me to get AC in one go!! :D

saurabh789: 2016-06-23 17:59:54

nice question my 50th!

sonali9696: 2016-06-22 21:01:44

My first thought was a 3D array for front,rear,age. But such large arrays can't be allocated.So think how age can be expressed in terms of front and rear and make 2D array for front,rear :) Happy coding!

saini428: 2016-06-13 03:06:54

simple recursion+memorization ,,,

Shivam Jha: 2016-06-01 12:46:21

a great tutorial for this by Michal Danilák .
https://www.quora.com/Are-there-any-good-resources-or-tutorials-for-dynamic-programming-besides-the-TopCoder-tutorial

Read the very first answer of this question.

atif_11: 2016-05-25 08:16:18

It's not a greedy problem.u consider this test case u will get the ans
6
10
100
1
1
1
12

vishalsingh: 2016-04-23 18:27:43

can anyone suggest test case where greedy approach fails

Nikki: 2016-03-20 20:28:16

For those who don't understand here is my explanation to them: All you need to do here is to find the maximum profit constraint is that you can choose either the most left or most right.

killjee_15: 2016-03-01 10:10:43

map+pair=>TLE
2-d array=>ac

coderkoko: 2016-02-01 14:07:24

Nice 1! My 2nd Dp! ^_^


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