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;
struct cww{cww(){ios::sync_with_stdio(false);cin.tie(0);}}star;
#define eb emplace_back
#define fi first
#define se second
#define chmax(a,b) if(a<b)a=b
typedef vector<int> vi;
typedef pair<int, int> pii;
void largest_rectangle_in_a_histogram() {
    int N; cin >> N;
    vector<int> h(N); rep(i, 0, N) { cin >> h[i]; }
    using P = pair<int, int>;
    stack<P> st;
    st.emplace(-1, -1);
    int ans = 0;
    rep(i, 0, N) {
        if (st.top().first == h[i])
            continue;
        int pos = i;
        while (st.top().first >= h[i]) {
            chmax(ans, st.top().first*(i - st.top().second));
            pos = st.top().second;
            st.pop();
        }
        st.emplace(h[i], pos);
    }
    while (st.size()) {
        chmax(ans, st.top().first*(N - st.top().second));
        st.pop();
    }
    cout << ans << endl;
}
 
signed main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    largest_rectangle_in_a_histogram();
    return 0;
}