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.
#include <bits/stdc++.h>
using namespace std;
template <typename T, class F = function<T(const T&, const T&)>>
class SparseTable {
 public:
  int n;
  vector<vector<T>> sp;
  F func;
  SparseTable(const vector<T>& a, const F& f) : func(f) {
    n = static_cast<int>(a.size());
    int max_log = 32 - __builtin_clz(n);
    sp.resize(max_log);
    sp[0] = a;
    for (int j = 1; j < max_log; ++j) {
      sp[j].resize(n - (1 << j) + 1);
      for (int i = 0; i <= n - (1 << j); ++i) {
        sp[j][i] = func(sp[j - 1][i], sp[j - 1][i + (1 << (j - 1))]);
      }
    }
  }
  T get(int l, int r) const {
    int lg = 32 - __builtin_clz(r - l + 1) - 1;
    return func(sp[lg][l], sp[lg][r - (1 << lg) + 1]);
  }
};
int main() {
  ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  int n;
  cin >> n;
  vector<int> a(n + 1), nxt(n + 1), prv(n + 1), cum(n + 1);
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    cum[i] = cum[i - 1] + a[i];
  }
  for (int i = n; i >= 1; i--) {
    nxt[i] = i + 1;
    while (nxt[i] <= n && a[nxt[i]] <= a[i]) nxt[i] = nxt[nxt[i]];
  }
  for (int i = 1; i <= n; i++) {
    prv[i] = i - 1;
    while (prv[i] >= 1 && a[prv[i]] <= a[i]) prv[i] = prv[prv[i]];
  }
  SparseTable<int> mn_sp(cum, [&](int i, int j) { return min(i, j); });
  SparseTable<int> mx_sp(cum, [&](int i, int j) { return max(i, j); });
  int ans = 0;
  for (int i = 1; i <= n; i++) {
    int l = prv[i] + 1, r = nxt[i] - 1;
    ans = max(ans, mx_sp.get(i, r) - mn_sp.get(l - 1, i - 1) - a[i]);
  }
  cout << ans;
}
