LogiQuest

198. Largest Rectangle in a Histogram

HardMonotonic Stack

Bars of width 1 have the given heights. Print the area of the largest rectangle that fits under the histogram.

Input format

Line 1: n Line 2: n heights

Output format

The largest area.

Example 1

Input

6
2 1 5 6 2 3

Output

10

Example 2

Input

2
2 4

Output

4

Constraints

1 ≤ n ≤ 10⁵ 0 ≤ heights ≤ 10⁴

Read input from standard input and print the answer to standard output. Your code is judged against 6 test cases, most of them hidden.

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