Bear and Bowling

6000ms

262144K

Description:

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, ..., s_k, total score is $\text{[math]}$ . 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?

Input:

The first line contains single integer n (1 ≤ n ≤ 10⁵).

The second line contains n space-separated integers a₁, a₂, ..., a_n (|a_i| ≤ 10⁷) - scores for Limak's rolls.

Output:

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

Sample Input:

5
-2 -8 0 5 -3

Sample Output:

Sample Input:

6
-10 20 -30 40 -50 60

Sample Output:

Note:

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.

Informação

Provedor Codeforces

Código CF573E