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 <vector>

using ll = long long;

int main() {
    int N;
    std::cin >> N;

    std::vector<ll> h(N);
    for (auto& e : h) std::cin >> e;
    h.push_back(0);

    ll ans = 0;
    std::vector<std::pair<ll, int>> stack;
    for (int i = 0; i <= N; ++i) {
        int pos = i;
        while (!stack.empty() && stack.back().first > h[i]) {
            auto p = stack.back();
            stack.pop_back();
            ans = std::max(ans, p.first * (i - p.second));
            pos = p.second;
        }
        if (stack.empty() || stack.back().first < h[i]) {
            stack.emplace_back(h[i], pos);
        }
    }

    std::cout << ans << std::endl;
    return 0;
}

