E. Bear and Bowling
data structures; greedy
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 s1, s2, ..., sk, total score is . Total score is 0 if there were no rolls.Limak made n rolls and got score ai 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?
The first line contains single integer n (1 ≤ n ≤ 105).The second line contains n space-separated integers a1, a2, ..., an (|ai| ≤ 107) - scores for Limak's rolls.
Print the maximum possible total score after choosing rolls to cancel.
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.