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 <cstdio>
#include <iostream>
#include <algorithm>
using namespace std;
static const int MAX_N = 100001;
static const int INFTY = 1000000001;
int n;
int h[MAX_N];
int L[MAX_N], R[MAX_N], st[MAX_N];

void solve() {
    int t = 0;
    for (int i = 0; i < n; i++) {
        while (t > 0 && h[st[t-1]] >= h[i]) t--;
        L[i] = (t == 0) ? 0 : (st[t-1] +1);
        st[t++] = i;
    }

    t = 0;
    for (int i = n - 1; i >= 0; i--) {
        while (t > 0 && h[st[t-1]] >= h[i]) t--;
        R[i] = (t == 0) ? n : st[t-1];
        st[t++] = i;
    }

    long long res = 0;
    for (int i = 0; i < n; i++) {
        res = max(res, (long long) h[i] * (R[i] - L[i]));
    }
    printf("%lld\n", res);
}


int main() {
    scanf("%d", &n);
    //fill(st, st+n+1, 0);
    for (int i = 0; i < n; i++) scanf("%d", &h[i]);
    solve();
    return 0;
}

