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.
import sys

input = sys.stdin.readline
flush = sys.stdout.flush

def buildM():
    for i in reversed(range(1, n)):
        segM[i] = max(segM[2*i], segM[2*i+1])
    return

def buildS():
    for i in reversed(range(1, n+1)):
        segSM[i] = max(segSM[2*i], segSM[2*i+1])
        segSm[i] = min(segSm[2*i], segSm[2*i+1])
    return

def queryM(l, r):
    res = -31
    l += n
    r += n
    while l < r:
        if l & 1:
            res = max(res, segM[l])
            l += 1
        if r & 1:
            r -= 1
            res = max(res, segM[r])
        l >>= 1
        r >>= 1
    return res

def querySM(l, r):
    res = -30 * 10**5 - 1
    l += n + 1
    r += n + 1
    while l < r:
        if l & 1:
            res = max(res, segSM[l])
            l += 1
        if r & 1:
            r -= 1
            res = max(res, segSM[r])
        l >>= 1
        r >>= 1
    return res

def querySm(l, r):
    res = 30 * 10**5 + 1
    l += n + 1
    r += n + 1
    while l < r:
        if l & 1:
            res = min(res, segSm[l])
            l += 1
        if r & 1:
            r -= 1
            res = min(res, segSm[r])
        l >>= 1
        r >>= 1
    return res

n = int(input())
a = list(map(int, input().split()))
S = [0] * (n + 1)
for i in range(n):
    S[i + 1] = S[i] + a[i]
segM = [0]*n + a
segSM = [0]*(n + 1) + S
segSm = [0]*(n + 1) + S
buildM()
buildS()

ans = -10**9
for i, x in enumerate(a):
    score = 0
    l = 0
    r = i
    while l < r:
        m = l + r >> 1
        if queryM(m, i + 1) == x:
            r = m
        else:
            l = m + 1
    ll = l
    l = i
    r = n - 1
    while l < r:
        m = (l + r >> 1) + 1
        if queryM(i, m + 1) == x:
            l = m
        else:
            r = m - 1
    rr = r
    score += S[i] - querySm(ll, i + 1)
    score += querySM(i + 1, rr + 2) - S[i + 1]
    if score > ans:
        ans = score
print(ans)
