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<typename T>
T largestRectangle(vector<T> &v) {
	stack<pair<T, int>> st;
	T maxv = 0;
	v.push_back(0);
	for (int i = 0; i < v.size(); i++) {
		int minv = i;
		while (!st.empty() && st.top().first > v[i]) {
			auto dat = st.top(); st.pop();
			maxv = max(maxv, dat.first * (i - dat.second));
			minv = min(minv, dat.second);
		}
		st.emplace(v[i], minv);
	}
	v.pop_back();
	return (maxv);
}

int main() {
	int N; cin >> N;
	vector<long long> H(N);
	for (auto &v : H) cin >> v;
	cout << largestRectangle(H) << endl;
	return (0);
}

