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
Diptesh Patel: 2014-09-29 09:47:28

what is wrong with case:12 ? :(

Kishlay Raj: 2014-09-22 14:27:12

my 50th cakewalk :P

Deepanker Aggarwal: 2014-09-20 16:50:58

50th :)...Btw any clues on how can this be done iteratively?

Arun Karthikeyan: 2014-09-13 19:54:33

Java Recursion TLE, same soln AC in C++
Java Iteration DP AC.

Gaurav Ahirwar: 2014-09-07 11:47:38

AC in go! cakewalk dp! :) :D ..

S: 2014-08-30 18:56:45

:S :D first attempt

tushar aggarwal: 2014-08-16 19:54:53

got it in 1st attempt :)

kernel: 2014-08-09 19:17:56

Instead of thinking it in terms of pure DP its better to approach the problem with recursion(TOPDOWN) with memoization...... AC

6 | 6 1 1 1 5 5 . Ans = 70 <- Greedy approach fails
5 | 1 3 1 5 2 . Ans = 43 <- Greedy approach works

Last edit: 2014-08-09 19:37:32
AmirShams: 2014-08-08 16:19:44

nice

Last edit: 2014-08-08 16:20:38

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