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.

""" Python 3 compatibility tools. """
from __future__ import division, print_function
import itertools
import sys
import os
from io import BytesIO, IOBase

if sys.version_info[0] < 3:
  input = raw_input
  range = xrange

  filter = itertools.ifilter
  map = itertools.imap
  zip = itertools.izip

def is_it_local():
  script_dir = str(os.getcwd()).split('/')
  username = "dipta007"
  return username in script_dir

def READ(fileName):
  if is_it_local():
    sys.stdin = open(f'./{fileName}', 'r')

# region fastio
BUFSIZE = 8192

class FastIO(IOBase):
  newlines = 0

  def __init__(self, file):
    self._fd = file.fileno()
    self.buffer = BytesIO()
    self.writable = "x" in file.mode or "r" not in file.mode
    self.write = self.buffer.write if self.writable else None

  def read(self):
    while True:
      b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
      if not b:
          break
      ptr = self.buffer.tell()
      self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
    self.newlines = 0
    return self.buffer.read()

  def readline(self):
    while self.newlines == 0:
      b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
      self.newlines = b.count(b"\n") + (not b)
      ptr = self.buffer.tell()
      self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
    self.newlines -= 1
    return self.buffer.readline()

  def flush(self):
    if self.writable:
      os.write(self._fd, self.buffer.getvalue())
      self.buffer.truncate(0), self.buffer.seek(0)

class IOWrapper(IOBase):
  def __init__(self, file):
    self.buffer = FastIO(file)
    self.flush = self.buffer.flush
    self.writable = self.buffer.writable
    self.write = lambda s: self.buffer.write(s.encode("ascii"))
    self.read = lambda: self.buffer.read().decode("ascii")
    self.readline = lambda: self.buffer.readline().decode("ascii")

if not is_it_local():
  sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
  input = lambda:...