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;
using i64 = int64_t;
using vi = vector<i64>;
using vvi = vector<vi>;

i64 largest_rectangle(vi hist) {
    hist.push_back(0);
    using ii = pair<i64, int>;
    stack<ii> st;
    i64 ret = 0;
    for (int i = 0; i < hist.size(); i++) {
        if (st.empty() || st.top().first < hist[i]) {
            st.push(ii(hist[i], i));
        } else {
            int s;
            while (st.size() && st.top().first >= hist[i]) {
                ret = max(ret, st.top().first * (i - st.top().second));
                s = st.top().second;
                st.pop();
            }
            st.push(ii(hist[i], s));
        }
    }
    
    return ret;
}

int main() {
    int n;
    cin >> n;
    vi as(n);
    for (int i = 0; i < n; i++) {
        cin >> as[i];
    }
    cout << largest_rectangle(as) << endl;
}
