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;
int main() {
    int N;
    cin >> N;
    vector<long long> h(N+1, 0);
    for (int i=0; i<N; ++i) cin >> h[i];
	long long mx = 0;
    stack<int> S, T;
    for (int i=0; i<=N; ++i) {
        while (!S.empty() && h[S.top()]>=h[i]) {
            mx = max(mx, h[S.top()]*(i-T.top()-1));
            S.pop(); T.pop();
        }
		T.push(S.empty() ? -1 : S.top());
		S.push(i); 
    }
    cout << mx << endl;
}
