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
n = int(input())
rects = list(map(int, input().split()))
rects.append(-1)
stack = []
ans = 0

for ind, rect in enumerate(rects):
#  print(stack)
  if not stack:
    stack.append((rect, ind))
  elif stack[-1][0] < rect:
    stack.append((rect, ind))
  elif stack[-1][0] == rect:
    continue
  else:
    while stack and stack[-1][0] > rect:
      prect, pind = stack.pop()
      ans = max(ans, prect * (ind - pind))
    stack.append((rect, pind))


print(ans)
