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>
#include<stack>
#include<algorithm>
using namespace std;
typedef long long int ll;

int main(){
	int N;
	cin >> N;
	vector<ll> h(N);
	for(int i = 0; i < N; i++) cin >> h[i];
	stack<int> stka, stkb;
	vector<int> memo(N), memo2(N);
	for(int i = 0; i < N; i++){
		while(!stka.empty() && h[stka.top()] >= h[i]) stka.pop();
		memo[i] = (stka.empty() ? 0 : stka.top() + 1);
		stka.push(i);
	}
	for(int i = N - 1; i >= 0; i--){
		while(!stkb.empty() && h[stkb.top()] >= h[i]) stkb.pop();
		memo2[i] = (stkb.empty() ? N : stkb.top());
		stkb.push(i);
	}
	ll res = 0;
	for(int i = 0; i < N; i++) res = max(res, h[i] * (ll)(memo2[i] - memo[i]));
	cout << res << endl;
	return 0;
}

