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

public class Main {
    public static void main(String[] args) throws IOException {
        FastScanner in = new FastScanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        new Main().run(in, out);
        out.close();
    }

    public static long mod = 17352642619633L;

    int N;
    int[] a;
    void run(FastScanner in, PrintWriter out) {

        N = in.nextInt();
        a = new int[N];

        for (int i = 0; i < N; i++) a[i] = in.nextInt();

        LinkedList<Integer> psums = new LinkedList<>();
        LinkedList<Integer> maxElem = new LinkedList<>();
        MinStack ms = new MinStack();

        psums.offerLast(0);
        maxElem.offerLast(0);
        ms.offerLast(0);

        int ans = 0;
        int psum = 0;

        for (int i = 0; i < N; i++) {
            psum += a[i];

            if (a[i] >= maxElem.peekLast()) {
                int min = Integer.MAX_VALUE;
                while (!maxElem.isEmpty() && a[i] >= maxElem.peekLast()) {
                    int lastPsum = psums.pollLast();
                    int lastMaxElem = maxElem.pollLast();

                    ms.pollLast(lastPsum + lastMaxElem);
                    min = Math.min(min, lastPsum);
                }

                psums.offerLast(min);
                maxElem.offerLast(a[i]);
                ms.offerLast(min+a[i]);
            }

            // System.out.println(Arrays.toString(psums.toArray()));
            // System.out.println(Arrays.toString(maxElem.toArray()));
            // System.out.println(Arrays.toString(ms.ms.toArray()));
            // System.out.println(psum - ms.getMin());
            // System.out.println();

            ans = Math.max(ans, psum - ms.getMin());

            psums.offerLast(psum);
            maxElem.offerLast(a[i]);
            ms.offerLast(psum + a[i]);
        }

        out.println(ans);
    }

    class MinStack {
        LinkedList<Integer> ms = new LinkedList<>();

        void offerLast(int x) {
            if (ms.isEmpty() || x <= ms.peekLast()) ms.offerLast(x);
        }

        void pollLast(int x) {
            if (ms.peekLast() == x) ms.pollLast();

        }

        int getMin() {
            return ms.peekLast();
        }

    }

    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
            st = null;
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }
    }
}
