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;

typedef pair<int,int> pii;
#define mp(x,y) (make_pair(x,y))

int main()
{
    int n;

    while(cin>>n)
    {
        vector<int> h(n),l(n),r(n);
        for(int i=0;i<n;i++)
        {
            cin>>h[i];
        }
        stack<pii> st;
        for(int i=0;i<n;i++)
        {
            while(!st.empty()&&st.top().first>=h[i])
            {
                st.pop();
            }
            if(!st.empty())
            {
                l[i]=st.top().second+1;
            }else
            {
                l[i]=0;
            }
            st.push(mp(h[i],i));
        }
        while(!st.empty())
        {
            st.pop();
        }
        for(int i=n-1;i>=0;i--)
        {
            while(!st.empty()&&st.top().first>=h[i])
            {
                st.pop();
            }
            if(!st.empty())
            {
                r[i]=st.top().second;
            }else
            {
                r[i]=n;
            }
            st.push(mp(h[i],i));
        }
        long long area=0;
        for(int i=0;i<n;i++)
        {
            area=max(area,1LL*h[i]*(r[i]-l[i]));
        }
        cout<<area<<endl;
    }

    return 0;
}

