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 <algorithm>
#include <queue>

using namespace std;

typedef long long ll;

struct Node {
   int index;
   ll value;
   Node(int index = 0, ll value = 0):index(index),value(value){
   }  
};

ll calHistrigramArea(const vector<ll>& a) {
    deque<Node> dq;
    ll ans = 0;
    for (int i = 0; i < a.size(); i++) {
        int e = a[i];
        while (!dq.empty()) {
            if (dq.back().value > e) {
                ll v = dq.back().value; dq.pop_back();
                int leftIndex = dq.empty() ? -1 : dq.back().index;
                ans = max(ans, (i - leftIndex - 1) * v);
            } else {
                break;
            }
        }
        dq.push_back(Node(i, e));
    }
    
    int i = a.size();
    while (!dq.empty()) {
        ll v = dq.back().value;dq.pop_back();
        int leftIndex = dq.empty() ? -1 : dq.back().index;
        ans = max(ans, (i - leftIndex - 1) * v);
    }
    return ans;
}


int main() {
    int n;
    cin >> n;
    vector<ll> a(n);
    
    for (int i = 0; i < n; i++) {
        cin >> a[i];
    }
    
    ll ans = calHistrigramArea(a);
    
    cout << ans << endl;
    
    return 0;
}