POJ 2559/hdu 1506 largest Rectangle in a histogram (DP)

Largest Rectangle in a histogram

http://poj.org/problem?id=2559

Time limit:1000ms

Memory limit:65536k

Description

A histogram is a polygon composed of a sequence of rectangles aligned in a common base line. The rectangles have equal widths but may have different. For example, the "figure on" the left shows the histogram, 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., the e.g of frequencies in characters. Note This order of the rectangles, i.e., their heights, is important. Calculate the area of the largest rectangle in a histogram this is aligned on the common base line, too. The figure on the right shows the largest aligned rectangle for the depicted histogram.

Input

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 compos Ed of. You are assume that 1<=n<=100000. Then follow n integersh₁,..., h_n, where 0<=h_i<=1000000000 . These numbers denote the heights's 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

For each test case output on a single line the ' largest rectangle in the specified histogram. Remember that this rectangle must is 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

Ideas:

Use 2 array r[i],l[i] to represent the left and right position of the largest rectangle with a h[i] height.

Attention:

Use the previously calculated r,l to speed up R[i],l[i's calculations (otherwise tle).