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 java.io.*;
import java.util.*;

import static java.lang.Math.*;

public class D {
    public static void main(String[] args) throws Exception {
        Scanner in = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int n = in.nextInt();
        int arr[] = new int[n + 2];
        for (int i = 1; i <= n; i++) {
            arr[i] = in.nextInt();
        }
        arr[0] = arr[n + 1] = 50;

        int lsum[] = new int[n + 2], rsum[] = new int[n + 2];
        int lrange[] = new int[n + 2], rrange[] = new int[n + 2];

        Stack<Integer> stack = new Stack<>();
        stack.add(0);
        for (int i = 1; i <= n; i++) {
            lsum[i] = arr[i] + lsum[i - 1];
            while (!stack.isEmpty() && arr[stack.peek()] <= arr[i]) stack.pop();
            lrange[i] = stack.peek() + 1;
            stack.add(i);
        }

        stack = new Stack<>();
        stack.add(n + 1);
        for (int i = n; i >= 1; i--) {
            rsum[i] = arr[i] + rsum[i + 1];
            while (!stack.isEmpty() && arr[stack.peek()] <= arr[i]) stack.pop();
            rrange[i] = stack.peek() - 1;
            stack.add(i);
        }


        SegTree_iterative LsumSeg = new SegTree_iterative(n + 5);
        SegTree_iterative RsumSeg = new SegTree_iterative(n + 5);

        for (int i = 1; i <= n; i++) {
            LsumSeg.update(i, lsum[i]);
            RsumSeg.update(i, rsum[i]);
        }

        int res = 0;
        for (int i = 1; i <= n; i++) {
            int left = RsumSeg.query(lrange[i], i) - rsum[i];
            int right = LsumSeg.query(i, rrange[i]) - lsum[i];
            res = max(res, left + right);
        }

        pw.println(res);


        pw.close();
    }

    static class SegTree_iterative {
        int t[];
        int n;

        SegTree_iterative(int N) { // 0-based indexing
            t = new int[2 * N];
            n = t.length;
        }

        public int get(int i) {
            return t[i + n / 2];
        }

        public int operation(int a, int b) {
            return max(a, b); // chane to min(a, b) or (a+b) for different ops
        }

        public void update(int i, int value) {
            i += n / 2;
            t[i] = value;
            for (; i > 1; i >>= 1)
                t[i >> 1] = operation(t[i], t[i ^ 1]);
        }

        public int query(int a, int b) {
            int res = (int) -1e9; // for sum, res = 0; for min, res = -inf ..etc
            for (a += n / 2, b += n / 2; a <= b; a = (a + 1) >> 1, b = (b - 1) >> 1) {
                if ((a & 1) != 0)
                    res = operation(res, t[a]);
                if ((b & 1) == 0)
                    res = operation(res, t[b]);
            }
            return res;
        }
    }

    static void debug(Object... obj) {
        System.err.println(Arrays.deepToString(obj));
    }
}