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 unsigned long long ull;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<double, double> pdd;
const ull mod = 1e9 + 7;
#define REP(i,n) for(int i=0;i<(int)n;++i)

ll renctanble_in_histgram(vector<ll> &h){
    h.push_back(0);
    ll res = 0;
    int N = h.size();
    stack<pll> st;
    REP(i, N){
        if(st.empty()){
            st.push(make_pair(h[i], i));
        }else{
            if(st.top().first < h[i]){
                st.push(make_pair(h[i], i));
            }
            if(st.top().first > h[i]){
                pll tmp_rect = st.top();
                while(!st.empty() && st.top().first >= h[i]){
                    tmp_rect = st.top();
                    res = max(res, tmp_rect.first * (i-tmp_rect.second));
                    st.pop();
                }
                st.push(make_pair(h[i], tmp_rect.second));
            }
        }
    }
    return res;
}

int main(){
    int N;
    cin >> N;
    vector<ll> h(N);
    REP(i, N) cin >> h[i];
    printf("%lld\n", renctanble_in_histgram(h));
    return 0;
}