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;

template<typename T>
T largest_rectangle(vector<T> &v) {
    int n = v.size();
    vector<int> L(n, -1);
    vector<int> R(n, n);
    // index, height
    using P = pair<int, T>;
    stack<P> sl;
    stack<P> sr;

    // L
    for (int i = n - 1; i >= 0; --i) {
        // stackに入っているより大きい要素を取り除く
        while (!sl.empty() && sl.top().second > v[i]) {
            // 現在のindexを渡す
            L[sl.top().first] = i;
            sl.pop();
        }
        // stackへ追加
        sl.emplace(i, v[i]);
    }

    // R
    for (int i = 0; i < n; ++i) {
        // stackに入っているより大きい要素を取り除く
        while (!sr.empty() && sr.top().second > v[i]) {
            // 現在のindexを渡す
            R[sr.top().first] = i;
            sr.pop();
        }
        // stackへ追加
        sr.emplace(i, v[i]);
    }

    T res = numeric_limits<T>::min();
    for (int i = 0; i < n; ++i) {
        res = max(res, v[i] * (R[i] - L[i] - 1));
    }
    return res;
}

/*
    verified https://onlinejudge.u-aizu.ac.jp/problems/DPL_3_C
*/
int main() {
    int N;
    cin >> N;
    vector<long long> h(N);
    for (int i = 0; i < N; ++i) cin >> h[i];
    cout << largest_rectangle(h) << endl;
}
