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;

#define MAX 100000+1

struct Rectangle{ int height;  int pos; };

int N;

long long getLargestRectangle( int size, int buffer[] )
{
	stack<Rectangle> S;
	long long maxv = 0;
	buffer[size] = 0;

	for( int i = 0; i <= size; i++ ) {
		Rectangle rect;
		rect.height = buffer[i];
		rect.pos = i;
		if ( S.empty() ) {
			S.push( rect );
		} else {
			if ( S.top().height < rect.height ) {
				S.push( rect );
			} else if ( S.top().height > rect.height ) {
				int target = i;
				while ( !S.empty() && S.top().height >= rect.height ) {
					Rectangle pre = S.top(); S.pop();
					long long area = (long long)pre.height * (i - pre.pos);
					maxv = max( maxv, area );
					target = pre.pos;
				}
				rect.pos = target;
				S.push(rect);
			}
		}
	}
	return maxv;
}

int h[MAX];

int main()
{
	cin >> N;
	for ( int i = 0; i < N; i++ ){
		cin >> h[i];
	}

	cout << getLargestRectangle( N, h ) << endl;;

	return 0;
}

