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
import sys
from collections import deque
readline = sys.stdin.readline
n = int(readline())
li = list(map(int, readline().split()))
def square(P):
    G = []
    L = deque()
    for i, v in enumerate(P):
        if not L:
            L.append((i, v))
            continue
        if v > L[-1][1]:
            L.append((i, v))
        elif v < L[-1][1]:
            k = i - 1
            while L and v < L[-1][1]:
                a = L.pop()
                G.append((k - a[0] + 1) * a[1])
            L.append((a[0], v))
    while L:
        a = L.pop()
        G.append((len(P) - a[0]) * a[1])
    return max(G)
print(square(li))