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;
using UL = unsigned int;
using ULL = unsigned long long;
using LL = long long;
#define rep(i, n) for(UL i = 0; i < (n); i++)

struct Problem {

    ULL A[100001];

    void Solve() {
        UL N; scanf("%d", &N);
        rep(i, N) scanf("%d", &A[i]);
        ULL ans = 0;
        deque<pair<ULL, UL>> Q;
        Q.push_back({ 0,0 });
        rep(i, N + 1) {
            UL p = i;
            while (Q.back().first > A[i]) {
                ans = max(ans, Q.back().first * (i - Q.back().second));
                p = Q.back().second;
                Q.pop_back();
            }
            Q.push_back({ A[i], p });
        }
        printf("%lld\n", ans);
    }
};
int main() {
    unique_ptr<Problem> p(new Problem());
    p->Solve();
    return 0;
}

