A13548. Yet Another Yet Another Task

Alice and Bob are playing yet another card game. This time the rules are the following. There are $n$ cards lying in a row in front of them. The $i$ -th card has value $a_i$ .

First, Alice chooses a non-empty consecutive segment of cards $[l; r]$ ( $l \le r$ ). After that Bob removes a single card $j$ from that segment $(l \le j \le r)$ . The score of the game is the total value of the remaining cards on the segment $(a_l + a_{l + 1} + \dots + a_{j - 1} + a_{j + 1} + \dots + a_{r - 1} + a_r)$ . In particular, if Alice chooses a segment with just one element, then the score after Bob removes the only card is $0$ .

Alice wants to make the score as big as possible. Bob takes such a card that the score is as small as possible.

What segment should Alice choose so that the score is maximum possible? Output the maximum score.

The first line contains a single integer $n$ ( $1 \le n \le 10^5$ ) — the number of cards.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ( $-30 \le a_i \le 30$ ) — the values on the cards.

Print a single integer — the final score of the game.

In the first example Alice chooses a segment $[1;5]$ — the entire row of cards. Bob removes card $3$ with the value $10$ from the segment. Thus, the final score is $5 + (-2) + (-1) + 4 = 6$ .

In the second example Alice chooses a segment $[1;4]$ , so that Bob removes either card $1$ or $3$ with the value $5$ , making the answer $5 + 2 + 3 = 10$ .

In the third example Alice can choose any of the segments of length $1$ : $[1;1]$ , $[2;2]$ or $[3;3]$ . Bob removes the only card, so the score is $0$ . If Alice chooses some other segment then the answer will be less than $0$ .