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;

template<class T> long long largest_rectangle (vector<T> a) {
    a.emplace_back(0);
    int n = a.size(); T ret = 0;
    stack<pair<T, int>> sta;
    for (int i = 0; i < n; i++) {
        if (sta.empty()) sta.emplace(a[i], i);
        else if (sta.top().first < a[i]) sta.emplace(a[i], i);
        else if (sta.top().first > a[i]) {
            int idx = i;
            while (!sta.empty()) {
                if (sta.top().first < a[i]) break;
                T h; int t; tie(h, t) = sta.top(); sta.pop();
                T s = h * (i - t); idx = t;
                if (ret < s) ret = s;
            }
            sta.emplace(a[i], idx);
        }
    }
    return ret;
}

int main() {
    int n;
    cin >> n;
    vector<long long> a(n);
    for (auto &e : a) cin >> e;

    cout << largest_rectangle(a) << '\n';

    return 0;
}
