p02328 Largest Rectangle in a Histogram
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
```python

"""
Writer:SPD_9X2
http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_3_C&lang=ja

ヒストグラム上の最大長方形
またdpかな…？
参考：
http://algorithms.blog55.fc2.com/blog-entry-132.html
"""
#最後に要素0を追加してくこと
def Largest_rectangle_in_histgram(lis):

    stk = []

    ans = 0
    N = len(lis)

    for i in range(N):

        if len(stk) == 0:
            stk.append((lis[i],i))

        elif stk[-1][0] < lis[i]:
            stk.append((lis[i],i))

        elif stk[-1][0] == lis[i]:
            pass

        else:
            lastpos = None
            while len(stk) > 0 and stk[-1][0] > lis[i]:

                nh,np = stk[-1]
                lastpos = np
                del stk[-1]

                ans = max(ans , nh*(i-np))

            stk.append((lis[i] , lastpos))

    return ans

N = int(input())
h = list(map(int,input().split()))
h.append(0)
print (Largest_rectangle_in_histgram(h))



```