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
sys.setrecursionlimit(2147483647)
INF=float("inf")
MOD=10**9+7
input=lambda:sys.stdin.readline().rstrip()
def resolve():
    n=int(input())
    IH=[(i,h) for i,h in enumerate(map(int,input().split()))]
    IH.append((n,0))
    ans=0
    Q=[[-1,0]]
    for i,h in IH:
        while(Q[-1][1]>h):
            i0,h0=Q.pop()
            ans=max(ans,h0*(i-Q[-1][0]-1))
        if(Q[-1][1]<h): Q.append([i,h])
        elif(Q[-1][1]==h): Q[-1][0]=i

    print(ans)
resolve()
