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 <cstdio>
#include <cstring>
#include <vector>
#include <deque>
#include <queue>
#include <array>
#include <set>
#include <map>
#include <cmath>
#include <complex>
#include <algorithm>
#include <numeric>
#include <utility>
#include <tuple>
#include <bitset>
#include <cstdint>
#include <cassert>
#include <random>
#include <iterator>

using namespace std;
using i64 = int64_t;
using i32 = int32_t;

template<class T>
i64 largest_rect(const T& h) {
    int n = h.size();
    vector<pair<int, i64>> stk;
    i64 ans = 0;
    for (int i = 0; i <= n; ++i) {
        int left = i;
        while (!stk.empty() && (i == n || h[i] < stk.back().second)) {
            left = stk.back().first;
            ans = max(ans, (i - left) * stk.back().second);
            stk.pop_back();
        }
        if (stk.empty() || (i != n && h[i] > stk.back().second)) {
            stk.emplace_back(left, h[i]);
        }
    }
    return ans;
}

int main() {
    i64 n;
    cin >> n;
    vector<i64> h(n);
    for (int i = 0; i < n; ++i) cin >> h[i];
    cout << largest_rect(h) << endl;
    return 0;
}
