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 <cmath>
#include <stack>
using namespace std;

using ll = long long;

int main() {
    int N;
    cin >> N;
    vector<ll> h(N);
    for(int i=0; i<N; ++i) {
        cin >> h[i];
    }
    stack<ll> st;
    vector<ll> l(N), r(N);
    for(int i=0; i<N; ++i) {
        while(!st.empty() && h[st.top()] >= h[i]) {
            st.pop();
        }
        l[i] = st.size() == 0 ? 0 : st.top()+1;
        st.push(i);
    }
    while(!st.empty()) {
        st.pop();
    }
    for(int i=N-1; i>=0; --i) {
        while(!st.empty() && h[st.top()] >= h[i]) {
            st.pop();
        }
        r[i] = st.size() == 0 ? N : st.top();
        st.push(i);
    }
    ll res = 0;
    for(int i=0; i<N; ++i) {
        res = max(res, h[i] * (r[i] - l[i]));
    }
    cout << res << endl;
}
