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.

Input

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.

Output

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

Note

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 $$$0$$$.

Yet Another Yet Another Task

Examples