8586: DPL_3_C : Largest Rectangle in a Histogram
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Description
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.
Input
The input is given in the following format.
$N$
$h_i = h_1,h_2,...,h_N$
Output
Print the area of the largest rectangle.
Constraints
$1≤N≤10^5$
$0≤h_i≤10^9$
$0≤h_i≤10^9$
Sample 1 Input
8
2 1 3 5 3 4 2 1
Sample 1 Output
12
Sample 2 Input
3
2 0 1
Sample 2 Output
2