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>
#define rep(i,n)for(int i=0;i<(n);i++)
using namespace std;
typedef long long ll;

int h[100000];
int L[100000],R[100000];

int main(){
	int n;scanf("%d",&n);
	rep(i,n)scanf("%d",&h[i]);
	stack<int>st;
	rep(i,n){
		while(!st.empty()&&h[st.top()]>=h[i])st.pop();
		if(st.empty())L[i]=0;
		else L[i]=st.top()+1;
		st.push(i);
	}
	while(!st.empty())st.pop();
	for(int i=n-1;i>=0;i--){
		while(!st.empty()&&h[st.top()]>=h[i])st.pop();
		if(st.empty())R[i]=n-1;
		else R[i]=st.top()-1;
		st.push(i);
	}
	ll Max=0;
	rep(i,n){
		Max=max(Max,(R[i]-L[i]+1)*(ll)h[i]);
	}
	cout<<Max<<endl;
}
