human
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 ≤ r). After that Bob removes a single card j from that segment (l ≤ j ≤ r). The score of the game is the total value of the remaining cards on the segment (a_l + a_{l + 1} + ... + a_{j - 1} + a_{j + 1} + ... + 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 ≤ n ≤ 10^5) — the number of cards.

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

Output

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

Examples

Input

5
5 -2 10 -1 4

Output

6

Input

8
5 2 5 3 -30 -30 6 9

Output

10

Input

3
-10 6 -15

Output

0

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.
 What is a Python program to print a single integer — the final score of the game?
assistant
#Here is Python program to print a single integer — the final score of the game.

import os
import sys
if os.path.exists('/mnt/c/Users/Square/square/codeforces'):
    f = iter(open('D.txt').readlines())
    def input():
        return next(f)
    # input = lambda: sys.stdin.readline().strip()  
else:
    input = lambda: sys.stdin.readline().strip()

fprint = lambda *args: print(*args, flush=True)

n = int(input())
A = list(map(int, input().split()))
ans = 0
for i in range(1, 31):
    res = 0
    for j in A:
        res += j
        if j > i:
            res = 0
        res = max(res, 0)
        ans = max(ans, res - i)
print(ans)