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,bisect
sys.setrecursionlimit(15000)
n = int(sys.stdin.readline())
a = list(map(int,sys.stdin.readline().split()))
a.append(0)

st = []
ar = 0
for i in range(n+1):
  if not st:
    st.append([i,a[i]])
  elif st[-1][1] < a[i]:
    st.append([i,a[i]])
  elif st[-1][1] == a[i]:
    st.append([i,a[i]])
  elif st[-1][1] > a[i]:
    while st and st[-1][1] >= a[i]:
      j,h = st.pop()
      ar = max(ar,(i-j)*(h))
    st.append([j,a[i]])
  #print(i,ar,st)
#print(a)
print(ar)
