A histogram is made of a number of contiguous bars, which have same width.

For a given histogram with $N$ bars which have a width of 1 and a height of $h_i$ = $h_1, h_2, ... , h_N$ respectively, find the area of the largest rectangular area.

Constraints

* $1 \leq N \leq 10^5$
* $0 \leq h_i \leq 10^9$

Input

The input is given in the following format.

$N$
$h_1$ $h_2$ ... $h_N$

Output

Print the area of the largest rectangle.

Examples

Input

8
2 1 3 5 3 4 2 1


Output

12


Input

3
2 0 1


Output

2
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < n; i++)

struct rec {int position; long height;};

int main() {
    int n;
    cin >> n;
    stack<rec> s;
    long max_area = 0;
    rep(i, n+1) {
        long h;
        if (i == n) h = 0;
        else cin >> h;
        if (s.empty()) {
            if (h > 0) s.push({i, h});
        } else {
            if (s.top().height < h) {
                s.push({i, h});
            } else if (s.top().height > h) {
                int left;
                while (not s.empty() && s.top().height >= h) {
                    long area = (i - s.top().position) * s.top().height;
                    max_area = max(max_area, area);
                    left = s.top().position;
                    s.pop();
                }
                if (h > 0) s.push({left, h});
            }
        }
    }
    cout << max_area << endl;
}
