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())
h = list(map(int, input().split( )))

Stk = []
Stk.append([h[0],1])
ans = []

for i in range(1,n):
    if Stk[-1][0] <= h[i]:
        Stk.append([h[i],1])
        
    else:
        tmp = 0
        while len(Stk) > 0 and Stk[-1][0]>h[i]:
            [hei,w] = Stk.pop()#Stk.pop()[0],Stk.pop()[1]だとpop2回することになるか
            tmp+=w
            ans.append(hei*tmp)
            
        Stk.append([h[i],tmp+1])
###以上だと最後appendした後の分が欠ける
tmp = 0
while len(Stk) > 0:
    [hei,w] = Stk.pop()
    tmp+=w
    ans.append(hei*tmp)

print(max(ans))
    
