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 <iostream>
#include <stack>

using namespace std;
using ULL = unsigned long long;

struct rect {
    ULL pos, height;
};

int main() {

    int N;
    cin >> N;

    ULL ans = 0;
    stack<rect> stk;

    for (int i = 0; i <= N; i++) {
        ULL p, h;
        p = i;
        if (i < N) cin >> h;
        else h = 0;
        if (stk.empty()) {
            stk.push((rect) {p, h});
        } else {
            if (stk.top().height < h) {
                stk.push((rect) {p, h});
            } else if (stk.top().height > h) {
                while (!stk.empty() && stk.top().height >= h) {
                    rect &pre = stk.top();
                    stk.pop();
                    ans = max(ans, pre.height * (i - pre.pos));
                    p = pre.pos;
                }
                stk.push((rect) {p, h});
            }
        }
    }

    cout << ans << endl;
}
