Bear and Bowling

题意翻译

- 给定一个长度为 $n$ 的序列 $a_{1\dots n}$。 - 你要求一个 $a$ 的子序列 $b_{1\dots m}$（可以为空），使得 $\sum_{i=1}^m ib_i$ 的值最大。 - $n \le 10^5$，$|a_i| \le 10^7$。

题目描述

Limak is an old brown bear. He often goes bowling with his friends. Today he feels really good and tries to beat his own record! For rolling a ball one gets a score — an integer (maybe negative) number of points. Score for $ i $ -th roll is multiplied by $ i $ and scores are summed up. So, for $ k $ rolls with scores $ s_{1},s_{2},...,s_{k} $ , total score is . Total score is $ 0 $ if there were no rolls. Limak made $ n $ rolls and got score $ a_{i} $ for $ i $ -th of them. He wants to maximize his total score and he came up with an interesting idea. He will cancel some rolls, saying that something distracted him or there was a strong wind. Limak is able to cancel any number of rolls, maybe even all or none of them. Total score is calculated as if there were only non-canceled rolls. Look at the sample tests for clarification. What maximum total score can Limak get?

输入输出格式

输入格式

The first line contains single integer $ n $ ( $ 1<=n<=10^{5} $ ). The second line contains $ n $ space-separated integers $ a_{1},a_{2},...,a_{n} $ ( $ |a_{i}|<=10^{7}) $ - scores for Limak's rolls.

输出格式

Print the maximum possible total score after choosing rolls to cancel.

输入输出样例

输入样例 #1

5
-2 -8 0 5 -3

输出样例 #1

13

输入样例 #2

6
-10 20 -30 40 -50 60

输出样例 #2

400

说明

In first sample Limak should cancel rolls with scores $ -8 $ and $ -3 $ . Then he is left with three rolls with scores $ -2,0,5 $ . Total score is $ 1·(-2)+2·0+3·5=13 $ . In second sample Limak should cancel roll with score $ -50 $ . Total score is $ 1·(-10)+2·20+3·(-30)+4·40+5·60=400 $ .