## HISTOGRA - Largest Rectangle in a Histogram

A histogram is a polygon composed of a sequence of rectangles aligned at a common base line. The rectangles have equal widths but may have different heights. For example, the figure on the left shows the histogram that consists of rectangles with the heights 2, 1, 4, 5, 1, 3, 3, measured in units where 1 is the width of the rectangles:

Usually, histograms are used to represent discrete distributions, e.g., the frequencies of characters in texts. Note that the order of the rectangles, i.e., their heights, is important. Calculate the area of the largest rectangle in a histogram that is aligned at the common base line, too. The figure on the right shows the largest aligned rectangle for the depicted histogram.

### Input Specification

The input contains several test cases. Each test case describes a histogram and starts with an integer `n`, denoting the number of rectangles it is composed of. You may assume that `1 <= n <= 100000`. Then follow `n` integers `h1, ..., hn`, where `0 <= hi <= 1000000000`. These numbers denote the heights of the rectangles of the histogram in left-to-right order. The width of each rectangle is `1`. A zero follows the input for the last test case.

### Output Specification

For each test case output on a single line the area of the largest rectangle in the specified histogram. Remember that this rectangle must be aligned at the common base line.

### Sample Input

```7 2 1 4 5 1 3 3
4 1000 1000 1000 1000
0
```

### Sample Output

```8
4000
```

hide comments
 karan_yadav: 2018-07-08 10:12:54 Use long long int. "I REPEAT USE LONG LONG INT" soham_12345: 2018-07-04 17:45:30 If you are planning to binary search on seg tree to find next lesser element DONT. It will TLE. Use stacks. kkislay20: 2018-06-27 18:47:44 Can someone please tell me whats wrong with my code. I'm getting WA however I have tried several testcases and all answers are correct. https://ide.geeksforgeeks.org/KKOz5CHeHJ rajcoolaryan: 2018-06-22 19:10:20 best question on stack megatron10599: 2018-06-18 14:19:19 Stack O(n) If you don't know about his already, then it is worth giving it some thinking time. Last edit: 2018-06-18 14:19:40 anshuman1117: 2018-06-09 09:11:30 @riddhi77 Did you use anything other than C/C++? aman_sachin200: 2018-06-05 21:49:07 Segment Tree Rocks!! pravirahuja: 2018-05-06 19:11:22 why do we need to use long long??? Someone please help... Last edit: 2018-05-06 19:45:18 riddhi77: 2018-02-11 09:16:39 https://ideone.com/P3lotL I am getting TLE......i used stack O(n)......worked correctly in another website (geeks for geeks)...but here it is showing tle. Pls help ashut0sh78: 2018-01-28 17:53:54 Last edit: 2018-01-28 18:00:39

 Added by: Wanderley GuimarÄƒes Date: 2007-09-21 Time limit: 0.800s Source limit: 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Languages: All except: ERL JS-RHINO Resource: University of Ulm Local Contest 2003