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 <algorithm>
#include <iostream>
#include <vector>
#include <stack>
using namespace std;

template <typename T>
long long largest_rectangle_hist(vector<T> &height) {
    stack<int> st;
    height.emplace_back(0);
    vector<int> left(height.size());
    long long ret = 0;
    for (int i = 0; i < height.size(); i++) {
        while (!st.empty() && height[st.top()] >= height[i]) {
            ret = max(ret, 1LL * (i - left[st.top()]) * height[st.top()]);
            st.pop();
        }
        left[i] = st.empty() ? 0 : st.top() + 1;
        st.emplace(i);
    }
    return ret;
}

int main() {
    int N; cin >> N;
    vector<int> h(N);
    for (int &hi: h) cin >> hi;
    cout << largest_rectangle_hist(h) << endl;
    return 0;
}
