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>
#include <cmath>

using namespace std;
typedef long long ll;
//typedef unsigned long long ll;

#define rep(i, n) for (int i = 0; i < (n); ++i)
//#define rep(i, n) for (ll i = 0; i < (n); ++i)
//#define sz(x) ll(x.size())
//typedef pair<ll, int> P;
typedef pair<ll, ll> P;
//const double INF = 1e10;
const ll INF = LONG_LONG_MAX / 10;
//const ll INF = (1ll << 31) - 1;
//const ll INF = 1e15;
const ll MINF = LONG_LONG_MIN;
//const int INF = INT_MAX / 10;
#define cmin(x, y) x = min(x, y)
#define cmax(x, y) x = max(x, y)
//typedef pair<int, int> P;
//typedef pair<double, double> P;

bool contain(set<P> &s, P a) { return s.find(a) != s.end(); }

//ifstream myfile("C:\\Users\\riku\\Downloads\\0_00.txt");
//ofstream outfile("log.txt");
//outfile << setw(6) << setfill('0') << prefecture << setw(6) << setfill('0') << rank << endl;
// std::cout << std::bitset<8>(9);
const int mod = 1000000007;


void print_line(vector<ll> &line) {
    if (line.size() == 0ll) {
        cout << endl;
        return;
    }
    for (ll i = 0; i < line.size(); i++) {
        cout << line[i];
        if (i == line.size() - 1) cout << endl;
        else cout << ' ';
    }
}

typedef priority_queue<long long, vector<long long>, greater<long long>> PQ_ASK;

struct Rectangle {
    ll start, height;
};

int main() {
    int w;
    cin >> w;

    vector<ll> histogram(w + 1, 0);

    rep(x, w) cin >> histogram[x];

    ll ans = 0;
    stack<Rectangle> s;
    rep(x, w + 1) {
        Rectangle rectangle;
        rectangle.start = x;
        rectangle.height = histogram[x];
        if (s.empty()) s.push(rectangle);
        else {
            if (s.top().height < rectangle.height) {
                s.push(rectangle);
            } else if (s.top().height > rectangle.height) {
                ll target = x;
                while (!s.empty() && s.top().height >= rectangle.height) {
                    Rectangle pre = s.top();
                    s.pop();
                    ll size = pre.height * (x - pre.start);
                    cmax(ans, size);
                    target = pre.start;
                }
                rectangle.start = target;
                s.push(rectangle);
            }
        }
    }
    cout << ans << endl;

}



