## 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
``` piyushhh: 2016-06-01 21:51:33 a good problem on stack implementation pamyjeela: 2016-05-18 11:58:05 there exists O(n) solution Last edit: 2016-05-18 12:03:44 karthik1997: 2016-05-08 13:10:22 dwij 28 ... Instead of linear search , why dont you try approach like segment trees for range minimum query , It would compress your complexity toO( N*log(N)).. By the way ,, use long long int guys...... Had a lot of wa coz of this :( Last edit: 2016-05-09 09:34:36 dwij28: 2016-04-26 15:30:37 Well I had to use stack. Divide and Conquer did not work for me. It gives a TLE. Divide and Conquer should be O(n^2) and not O(nlog(n)). I did a linear search in the code for my crossing part. Binary search does not seem viable as the array is not sorted. Correct me if I am wrong. lamduong: 2016-04-15 06:35:37 used greedy algorithm and time limited :-( Last edit: 2016-04-15 06:37:07 nonushikhar: 2016-03-10 19:07:03 finally ac :) try2catch: 2016-01-26 15:24:53 if doing with stack don't use java. Gives TLE bcoz! lakshay_v06: 2016-01-22 11:33:23 One of the best adhoc questions! Divide and Conquer : O(nlogn) Stack : O(n) impossible_1: 2016-01-01 10:21:29 take the problem easy. Govind Lahoti: 2015-12-30 13:08:13 nice problem :)