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

inputFormat

Input

The input is given in the following format.

$N$ $h_1$ $h_2$ ... $h_N$

outputFormat

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

样例

8
2 1 3 5 3 4 2 1

12