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
if sys.subversion[0] == "PyPy":
    import io, atexit
    sys.stdout = io.BytesIO()
    atexit.register(lambda: sys.__stdout__.write(sys.stdout.getvalue()))
    
    sys.stdin = io.BytesIO(sys.stdin.read())
    input = lambda: sys.stdin.readline().rstrip()
 
RS = raw_input
RI = lambda x=int: map(x,RS().split())
RN = lambda x=int: x(RS())
''' ...................................................................... '''
from sys import setrecursionlimit as srl
srl(10**5)

# generalised approch using D&C
# Expected Complexity - O(NlogN)
# Worst Case - O(N^2)

def maxCrossSum(arr,lo,mid,hi):

    # <-- Leftwards movement
    tot,lefty,pos1 = 0,0,mid

    for i in xrange(mid-1,lo-1,-1):
        if arr[i]>arr[mid]: break
        tot += arr[i]
        if tot>lefty:
            lefty = tot
            pos1 = i

    # --> Rightwards Movement
    tot,righty,pos2 = 0,0,mid

    for i in xrange(mid+1,hi+1):
        if arr[i]>arr[mid]: break
        tot += arr[i]
        if tot>righty:
            righty = tot
            pos2 = i

    return lefty+righty,pos1,pos2

def solve(arr,l,r):
    if l>=r: return 0
    m = l
    cen = (l+r)/2
    for i in xrange(l+1,r+1):
        if arr[i]==arr[m]:  # Can also use randomisation
            if abs(cen-i)<abs(cen-m):
                m = i
        elif arr[i]>arr[m]: m = i

    if arr[m]<=0: return 0

    v1,l1,r1 = maxCrossSum(arr,l,m,r)
    #print '%d %d %d'%(l1,r1,v1)
    v2 = solve(arr,l,m-1)
    v3 = solve(arr,m+1,r)
    return max(v1,v2,v3)

n = RN()
arr = RI()
print solve(arr,0,n-1)
