Treats for the Cows
시간 제한1초메모리 제한1024 MB
N개의 간식이 일렬로 놓여 있을 때 매일 양쪽 끝 중 하나를 꺼내 팔고, k일째 판 간식은 값에 k를 곱한 만큼 받는다. 총수입의 최댓값을 구한다.
문제
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.
입력
- Line 1: A single integer, N
- Lines 2..N+1: Line i+1 contains the value of treat v(i)
출력
- Line 1: The maximum revenue FJ can achieve by selling the treats