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# Largest Rectangle in Histogram

Problem Description

Given an array of integers A .

A represents a histogram i.e A[i] denotes height of the ith histogram's bar. Width of each bar is 1.

Find the area of the largest rectangle formed by the histogram.

Problem Constraints

1 <= |A| <= 100000

1 <= A[i] <= 1000000000

Input Format

The only argument given is the integer array A.

Output Format

Return the area of largest rectangle in the histogram.

Example Input

Input 1:

``` A = [2, 1, 5, 6, 2, 3]
```

Input 2:

``` A = [2]
```

Example Output

Output 1:

``` 10
```

Output 2:

``` 2
```

Example Explanation

Explanation 1:

```The largest rectangle has area = 10 unit. Formed by A[3] to A[4].
```

Explanation 2:

```Largest rectangle has area 2.
```

NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a question? Checkout Sample Codes for more details.
Hints
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## Discussion

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