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
vijayrit: 2017-05-10 11:41:58

a good question to improve in recursion and memoization

alaa_alrayes96: 2017-04-08 09:32:25

simple recursion + memo got acc

sirjan13: 2017-03-28 19:51:24

simple recursion + memo did the trick!!

mddaud001: 2017-03-25 20:02:04

Top-Down + Memo
AC in one GO:)

amandal799: 2017-03-24 22:30:02

simple recursion and memorization and AC in one go

rishi_07: 2017-03-03 12:30:59

Very Nice Question!

hasan356: 2017-03-02 18:27:24

My first memo!!

vladimira: 2017-02-25 15:44:05

Can be implemented easily with just O(n) memory without some matrix chain multiplications. But you must work first with your pen and sheet of paper a little. My solving function was 10 lines.

nilabja16180: 2017-02-22 19:02:54

Not easy as it seems!

sarthakshah30: 2017-01-27 19:49:22

AC in one Go ;)
Bottom Up DP
Hint ->Matrix chain Multiplication Variation


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