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;
using P = pair<int, int>;

int main()
{
	int N;
	cin >> N;
	vector<int> h(N + 2), mi(N + 2), ma(N + 2);
	for (int i = 1; i <= N; i++) {
		cin >> h[i];
	}
	vector<P> st;
	for (int i = 1; i <= N + 1; i++) {
		while (!st.empty() && st.back().second > h[i]) {
			ma[st.back().first] = i - 1;
			st.pop_back();
		}
		st.push_back(P(i, h[i]));
	}
	st.clear();
	for (int i = N; i >= 0; i--) {
		while (!st.empty() && st.back().second > h[i]) {
			mi[st.back().first] = i + 1;
			st.pop_back();
		}
		st.push_back(P(i, h[i]));
	}
	long long res = 0;
	for (int i = 1; i <= N; i++) {
		res = max(res, (long long)(ma[i] - mi[i] + 1) * h[i]);
	}
	cout << res << endl;
	return 0;
}